Package org.joml

Class Intersectionf


  • public class Intersectionf
    extends java.lang.Object
    Contains intersection and distance tests for some 2D and 3D geometric primitives.
    Author:
    Kai Burjack
    • Constructor Detail

      • Intersectionf

        public Intersectionf()
    • Method Detail

      • testPlaneSphere

        public static boolean testPlaneSphere​(float a,
                                              float b,
                                              float c,
                                              float d,
                                              float centerX,
                                              float centerY,
                                              float centerZ,
                                              float radius)
        Test whether the plane with the general plane equation a*x + b*y + c*z + d = 0 intersects the sphere with center (centerX, centerY, centerZ) and radius.

        Reference: http://math.stackexchange.com

        Parameters:
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the z factor in the plane equation
        d - the constant in the plane equation
        centerX - the x coordinate of the sphere's center
        centerY - the y coordinate of the sphere's center
        centerZ - the z coordinate of the sphere's center
        radius - the radius of the sphere
        Returns:
        true iff the plane intersects the sphere; false otherwise
      • testPlaneSphere

        public static boolean testPlaneSphere​(Planef plane,
                                              Spheref sphere)
        Test whether the given plane intersects the given sphere with center.

        Reference: http://math.stackexchange.com

        Parameters:
        plane - the plane
        sphere - the sphere
        Returns:
        true iff the plane intersects the sphere; false otherwise
      • intersectPlaneSphere

        public static boolean intersectPlaneSphere​(float a,
                                                   float b,
                                                   float c,
                                                   float d,
                                                   float centerX,
                                                   float centerY,
                                                   float centerZ,
                                                   float radius,
                                                   Vector4f intersectionCenterAndRadius)
        Test whether the plane with the general plane equation a*x + b*y + c*z + d = 0 intersects the sphere with center (centerX, centerY, centerZ) and radius, and store the center of the circle of intersection in the (x, y, z) components of the supplied vector and the radius of that circle in the w component.

        Reference: http://math.stackexchange.com

        Parameters:
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the z factor in the plane equation
        d - the constant in the plane equation
        centerX - the x coordinate of the sphere's center
        centerY - the y coordinate of the sphere's center
        centerZ - the z coordinate of the sphere's center
        radius - the radius of the sphere
        intersectionCenterAndRadius - will hold the center of the circle of intersection in the (x, y, z) components and the radius in the w component
        Returns:
        true iff the plane intersects the sphere; false otherwise
      • intersectPlaneSweptSphere

        public static boolean intersectPlaneSweptSphere​(float a,
                                                        float b,
                                                        float c,
                                                        float d,
                                                        float cX,
                                                        float cY,
                                                        float cZ,
                                                        float radius,
                                                        float vX,
                                                        float vY,
                                                        float vZ,
                                                        Vector4f pointAndTime)
        Test whether the plane with the general plane equation a*x + b*y + c*z + d = 0 intersects the moving sphere with center (cX, cY, cZ), radius and velocity (vX, vY, vZ), and store the point of intersection in the (x, y, z) components of the supplied vector and the time of intersection in the w component.

        The normal vector (a, b, c) of the plane equation needs to be normalized.

        Reference: Book "Real-Time Collision Detection" chapter 5.5.3 "Intersecting Moving Sphere Against Plane"

        Parameters:
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the z factor in the plane equation
        d - the constant in the plane equation
        cX - the x coordinate of the center position of the sphere at t=0
        cY - the y coordinate of the center position of the sphere at t=0
        cZ - the z coordinate of the center position of the sphere at t=0
        radius - the sphere's radius
        vX - the x component of the velocity of the sphere
        vY - the y component of the velocity of the sphere
        vZ - the z component of the velocity of the sphere
        pointAndTime - will hold the point and time of intersection (if any)
        Returns:
        true iff the sphere intersects the plane; false otherwise
      • testPlaneSweptSphere

        public static boolean testPlaneSweptSphere​(float a,
                                                   float b,
                                                   float c,
                                                   float d,
                                                   float t0X,
                                                   float t0Y,
                                                   float t0Z,
                                                   float r,
                                                   float t1X,
                                                   float t1Y,
                                                   float t1Z)
        Test whether the plane with the general plane equation a*x + b*y + c*z + d = 0 intersects the sphere moving from center position (t0X, t0Y, t0Z) to (t1X, t1Y, t1Z) and having the given radius.

        The normal vector (a, b, c) of the plane equation needs to be normalized.

        Reference: Book "Real-Time Collision Detection" chapter 5.5.3 "Intersecting Moving Sphere Against Plane"

        Parameters:
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the z factor in the plane equation
        d - the constant in the plane equation
        t0X - the x coordinate of the start position of the sphere
        t0Y - the y coordinate of the start position of the sphere
        t0Z - the z coordinate of the start position of the sphere
        r - the sphere's radius
        t1X - the x coordinate of the end position of the sphere
        t1Y - the y coordinate of the end position of the sphere
        t1Z - the z coordinate of the end position of the sphere
        Returns:
        true if the sphere intersects the plane; false otherwise
      • testAabPlane

        public static boolean testAabPlane​(float minX,
                                           float minY,
                                           float minZ,
                                           float maxX,
                                           float maxY,
                                           float maxZ,
                                           float a,
                                           float b,
                                           float c,
                                           float d)
        Test whether the axis-aligned box with minimum corner (minX, minY, minZ) and maximum corner (maxX, maxY, maxZ) intersects the plane with the general equation a*x + b*y + c*z + d = 0.

        Reference: http://www.lighthouse3d.com ("Geometric Approach - Testing Boxes II")

        Parameters:
        minX - the x coordinate of the minimum corner of the axis-aligned box
        minY - the y coordinate of the minimum corner of the axis-aligned box
        minZ - the z coordinate of the minimum corner of the axis-aligned box
        maxX - the x coordinate of the maximum corner of the axis-aligned box
        maxY - the y coordinate of the maximum corner of the axis-aligned box
        maxZ - the z coordinate of the maximum corner of the axis-aligned box
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the z factor in the plane equation
        d - the constant in the plane equation
        Returns:
        true iff the axis-aligned box intersects the plane; false otherwise
      • testAabPlane

        public static boolean testAabPlane​(AABBf aabb,
                                           Planef plane)
        Test whether the axis-aligned box intersects the plane.

        Reference: http://www.lighthouse3d.com ("Geometric Approach - Testing Boxes II")

        Parameters:
        aabb - the AABB
        plane - the plane
        Returns:
        true iff the axis-aligned box intersects the plane; false otherwise
      • testAabPlane

        public static boolean testAabPlane​(Vector3fc min,
                                           Vector3fc max,
                                           float a,
                                           float b,
                                           float c,
                                           float d)
        Test whether the axis-aligned box with minimum corner min and maximum corner max intersects the plane with the general equation a*x + b*y + c*z + d = 0.

        Reference: http://www.lighthouse3d.com ("Geometric Approach - Testing Boxes II")

        Parameters:
        min - the minimum corner of the axis-aligned box
        max - the maximum corner of the axis-aligned box
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the z factor in the plane equation
        d - the constant in the plane equation
        Returns:
        true iff the axis-aligned box intersects the plane; false otherwise
      • testAabAab

        public static boolean testAabAab​(float minXA,
                                         float minYA,
                                         float minZA,
                                         float maxXA,
                                         float maxYA,
                                         float maxZA,
                                         float minXB,
                                         float minYB,
                                         float minZB,
                                         float maxXB,
                                         float maxYB,
                                         float maxZB)
        Test whether the axis-aligned box with minimum corner (minXA, minYA, minZA) and maximum corner (maxXA, maxYA, maxZA) intersects the axis-aligned box with minimum corner (minXB, minYB, minZB) and maximum corner (maxXB, maxYB, maxZB).
        Parameters:
        minXA - the x coordinate of the minimum corner of the first axis-aligned box
        minYA - the y coordinate of the minimum corner of the first axis-aligned box
        minZA - the z coordinate of the minimum corner of the first axis-aligned box
        maxXA - the x coordinate of the maximum corner of the first axis-aligned box
        maxYA - the y coordinate of the maximum corner of the first axis-aligned box
        maxZA - the z coordinate of the maximum corner of the first axis-aligned box
        minXB - the x coordinate of the minimum corner of the second axis-aligned box
        minYB - the y coordinate of the minimum corner of the second axis-aligned box
        minZB - the z coordinate of the minimum corner of the second axis-aligned box
        maxXB - the x coordinate of the maximum corner of the second axis-aligned box
        maxYB - the y coordinate of the maximum corner of the second axis-aligned box
        maxZB - the z coordinate of the maximum corner of the second axis-aligned box
        Returns:
        true iff both axis-aligned boxes intersect; false otherwise
      • testAabAab

        public static boolean testAabAab​(Vector3fc minA,
                                         Vector3fc maxA,
                                         Vector3fc minB,
                                         Vector3fc maxB)
        Test whether the axis-aligned box with minimum corner minA and maximum corner maxA intersects the axis-aligned box with minimum corner minB and maximum corner maxB.
        Parameters:
        minA - the minimum corner of the first axis-aligned box
        maxA - the maximum corner of the first axis-aligned box
        minB - the minimum corner of the second axis-aligned box
        maxB - the maximum corner of the second axis-aligned box
        Returns:
        true iff both axis-aligned boxes intersect; false otherwise
      • testAabAab

        public static boolean testAabAab​(AABBf aabb1,
                                         AABBf aabb2)
        Test whether the two axis-aligned boxes intersect.
        Parameters:
        aabb1 - the first AABB
        aabb2 - the second AABB
        Returns:
        true iff both axis-aligned boxes intersect; false otherwise
      • testObOb

        public static boolean testObOb​(Vector3f b0c,
                                       Vector3f b0uX,
                                       Vector3f b0uY,
                                       Vector3f b0uZ,
                                       Vector3f b0hs,
                                       Vector3f b1c,
                                       Vector3f b1uX,
                                       Vector3f b1uY,
                                       Vector3f b1uZ,
                                       Vector3f b1hs)
        Test whether two oriented boxes given via their center position, orientation and half-size, intersect.

        The orientation of a box is given as three unit vectors spanning the local orthonormal basis of the box.

        The size is given as the half-size along each of the unit vectors defining the orthonormal basis.

        Reference: Book "Real-Time Collision Detection" chapter 4.4.1 "OBB-OBB Intersection"

        Parameters:
        b0c - the center of the first box
        b0uX - the local X unit vector of the first box
        b0uY - the local Y unit vector of the first box
        b0uZ - the local Z unit vector of the first box
        b0hs - the half-size of the first box
        b1c - the center of the second box
        b1uX - the local X unit vector of the second box
        b1uY - the local Y unit vector of the second box
        b1uZ - the local Z unit vector of the second box
        b1hs - the half-size of the second box
        Returns:
        true if both boxes intersect; false otherwise
      • testObOb

        public static boolean testObOb​(float b0cX,
                                       float b0cY,
                                       float b0cZ,
                                       float b0uXx,
                                       float b0uXy,
                                       float b0uXz,
                                       float b0uYx,
                                       float b0uYy,
                                       float b0uYz,
                                       float b0uZx,
                                       float b0uZy,
                                       float b0uZz,
                                       float b0hsX,
                                       float b0hsY,
                                       float b0hsZ,
                                       float b1cX,
                                       float b1cY,
                                       float b1cZ,
                                       float b1uXx,
                                       float b1uXy,
                                       float b1uXz,
                                       float b1uYx,
                                       float b1uYy,
                                       float b1uYz,
                                       float b1uZx,
                                       float b1uZy,
                                       float b1uZz,
                                       float b1hsX,
                                       float b1hsY,
                                       float b1hsZ)
        Test whether two oriented boxes given via their center position, orientation and half-size, intersect.

        The orientation of a box is given as three unit vectors spanning the local orthonormal basis of the box.

        The size is given as the half-size along each of the unit vectors defining the orthonormal basis.

        Reference: Book "Real-Time Collision Detection" chapter 4.4.1 "OBB-OBB Intersection"

        Parameters:
        b0cX - the x coordinate of the center of the first box
        b0cY - the y coordinate of the center of the first box
        b0cZ - the z coordinate of the center of the first box
        b0uXx - the x coordinate of the local X unit vector of the first box
        b0uXy - the y coordinate of the local X unit vector of the first box
        b0uXz - the z coordinate of the local X unit vector of the first box
        b0uYx - the x coordinate of the local Y unit vector of the first box
        b0uYy - the y coordinate of the local Y unit vector of the first box
        b0uYz - the z coordinate of the local Y unit vector of the first box
        b0uZx - the x coordinate of the local Z unit vector of the first box
        b0uZy - the y coordinate of the local Z unit vector of the first box
        b0uZz - the z coordinate of the local Z unit vector of the first box
        b0hsX - the half-size of the first box along its local X axis
        b0hsY - the half-size of the first box along its local Y axis
        b0hsZ - the half-size of the first box along its local Z axis
        b1cX - the x coordinate of the center of the second box
        b1cY - the y coordinate of the center of the second box
        b1cZ - the z coordinate of the center of the second box
        b1uXx - the x coordinate of the local X unit vector of the second box
        b1uXy - the y coordinate of the local X unit vector of the second box
        b1uXz - the z coordinate of the local X unit vector of the second box
        b1uYx - the x coordinate of the local Y unit vector of the second box
        b1uYy - the y coordinate of the local Y unit vector of the second box
        b1uYz - the z coordinate of the local Y unit vector of the second box
        b1uZx - the x coordinate of the local Z unit vector of the second box
        b1uZy - the y coordinate of the local Z unit vector of the second box
        b1uZz - the z coordinate of the local Z unit vector of the second box
        b1hsX - the half-size of the second box along its local X axis
        b1hsY - the half-size of the second box along its local Y axis
        b1hsZ - the half-size of the second box along its local Z axis
        Returns:
        true if both boxes intersect; false otherwise
      • intersectSphereSphere

        public static boolean intersectSphereSphere​(float aX,
                                                    float aY,
                                                    float aZ,
                                                    float radiusSquaredA,
                                                    float bX,
                                                    float bY,
                                                    float bZ,
                                                    float radiusSquaredB,
                                                    Vector4f centerAndRadiusOfIntersectionCircle)
        Test whether the one sphere with center (aX, aY, aZ) and square radius radiusSquaredA intersects the other sphere with center (bX, bY, bZ) and square radius radiusSquaredB, and store the center of the circle of intersection in the (x, y, z) components of the supplied vector and the radius of that circle in the w component.

        The normal vector of the circle of intersection can simply be obtained by subtracting the center of either sphere from the other.

        Reference: http://gamedev.stackexchange.com

        Parameters:
        aX - the x coordinate of the first sphere's center
        aY - the y coordinate of the first sphere's center
        aZ - the z coordinate of the first sphere's center
        radiusSquaredA - the square of the first sphere's radius
        bX - the x coordinate of the second sphere's center
        bY - the y coordinate of the second sphere's center
        bZ - the z coordinate of the second sphere's center
        radiusSquaredB - the square of the second sphere's radius
        centerAndRadiusOfIntersectionCircle - will hold the center of the circle of intersection in the (x, y, z) components and the radius in the w component
        Returns:
        true iff both spheres intersect; false otherwise
      • intersectSphereSphere

        public static boolean intersectSphereSphere​(Vector3fc centerA,
                                                    float radiusSquaredA,
                                                    Vector3fc centerB,
                                                    float radiusSquaredB,
                                                    Vector4f centerAndRadiusOfIntersectionCircle)
        Test whether the one sphere with center centerA and square radius radiusSquaredA intersects the other sphere with center centerB and square radius radiusSquaredB, and store the center of the circle of intersection in the (x, y, z) components of the supplied vector and the radius of that circle in the w component.

        The normal vector of the circle of intersection can simply be obtained by subtracting the center of either sphere from the other.

        Reference: http://gamedev.stackexchange.com

        Parameters:
        centerA - the first sphere's center
        radiusSquaredA - the square of the first sphere's radius
        centerB - the second sphere's center
        radiusSquaredB - the square of the second sphere's radius
        centerAndRadiusOfIntersectionCircle - will hold the center of the circle of intersection in the (x, y, z) components and the radius in the w component
        Returns:
        true iff both spheres intersect; false otherwise
      • intersectSphereSphere

        public static boolean intersectSphereSphere​(Spheref sphereA,
                                                    Spheref sphereB,
                                                    Vector4f centerAndRadiusOfIntersectionCircle)
        Test whether the one sphere with intersects the other sphere, and store the center of the circle of intersection in the (x, y, z) components of the supplied vector and the radius of that circle in the w component.

        The normal vector of the circle of intersection can simply be obtained by subtracting the center of either sphere from the other.

        Reference: http://gamedev.stackexchange.com

        Parameters:
        sphereA - the first sphere
        sphereB - the second sphere
        centerAndRadiusOfIntersectionCircle - will hold the center of the circle of intersection in the (x, y, z) components and the radius in the w component
        Returns:
        true iff both spheres intersect; false otherwise
      • intersectSphereTriangle

        public static int intersectSphereTriangle​(float sX,
                                                  float sY,
                                                  float sZ,
                                                  float sR,
                                                  float v0X,
                                                  float v0Y,
                                                  float v0Z,
                                                  float v1X,
                                                  float v1Y,
                                                  float v1Z,
                                                  float v2X,
                                                  float v2Y,
                                                  float v2Z,
                                                  Vector3f result)
        Test whether the given sphere with center (sX, sY, sZ) intersects the triangle given by its three vertices, and if they intersect store the point of intersection into result.

        This method also returns whether the point of intersection is on one of the triangle's vertices, edges or on the face.

        Reference: Book "Real-Time Collision Detection" chapter 5.2.7 "Testing Sphere Against Triangle"

        Parameters:
        sX - the x coordinate of the sphere's center
        sY - the y coordinate of the sphere's center
        sZ - the z coordinate of the sphere's center
        sR - the sphere's radius
        v0X - the x coordinate of the first vertex of the triangle
        v0Y - the y coordinate of the first vertex of the triangle
        v0Z - the z coordinate of the first vertex of the triangle
        v1X - the x coordinate of the second vertex of the triangle
        v1Y - the y coordinate of the second vertex of the triangle
        v1Z - the z coordinate of the second vertex of the triangle
        v2X - the x coordinate of the third vertex of the triangle
        v2Y - the y coordinate of the third vertex of the triangle
        v2Z - the z coordinate of the third vertex of the triangle
        result - will hold the point of intersection
        Returns:
        one of POINT_ON_TRIANGLE_VERTEX_0, POINT_ON_TRIANGLE_VERTEX_1, POINT_ON_TRIANGLE_VERTEX_2, POINT_ON_TRIANGLE_EDGE_01, POINT_ON_TRIANGLE_EDGE_12, POINT_ON_TRIANGLE_EDGE_20 or POINT_ON_TRIANGLE_FACE or 0
      • testSphereSphere

        public static boolean testSphereSphere​(float aX,
                                               float aY,
                                               float aZ,
                                               float radiusSquaredA,
                                               float bX,
                                               float bY,
                                               float bZ,
                                               float radiusSquaredB)
        Test whether the one sphere with center (aX, aY, aZ) and square radius radiusSquaredA intersects the other sphere with center (bX, bY, bZ) and square radius radiusSquaredB.

        Reference: http://gamedev.stackexchange.com

        Parameters:
        aX - the x coordinate of the first sphere's center
        aY - the y coordinate of the first sphere's center
        aZ - the z coordinate of the first sphere's center
        radiusSquaredA - the square of the first sphere's radius
        bX - the x coordinate of the second sphere's center
        bY - the y coordinate of the second sphere's center
        bZ - the z coordinate of the second sphere's center
        radiusSquaredB - the square of the second sphere's radius
        Returns:
        true iff both spheres intersect; false otherwise
      • testSphereSphere

        public static boolean testSphereSphere​(Vector3fc centerA,
                                               float radiusSquaredA,
                                               Vector3fc centerB,
                                               float radiusSquaredB)
        Test whether the one sphere with center centerA and square radius radiusSquaredA intersects the other sphere with center centerB and square radius radiusSquaredB.

        Reference: http://gamedev.stackexchange.com

        Parameters:
        centerA - the first sphere's center
        radiusSquaredA - the square of the first sphere's radius
        centerB - the second sphere's center
        radiusSquaredB - the square of the second sphere's radius
        Returns:
        true iff both spheres intersect; false otherwise
      • distancePointPlane

        public static float distancePointPlane​(float pointX,
                                               float pointY,
                                               float pointZ,
                                               float a,
                                               float b,
                                               float c,
                                               float d)
        Determine the signed distance of the given point (pointX, pointY, pointZ) to the plane specified via its general plane equation a*x + b*y + c*z + d = 0.
        Parameters:
        pointX - the x coordinate of the point
        pointY - the y coordinate of the point
        pointZ - the z coordinate of the point
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the z factor in the plane equation
        d - the constant in the plane equation
        Returns:
        the distance between the point and the plane
      • distancePointPlane

        public static float distancePointPlane​(float pointX,
                                               float pointY,
                                               float pointZ,
                                               float v0X,
                                               float v0Y,
                                               float v0Z,
                                               float v1X,
                                               float v1Y,
                                               float v1Z,
                                               float v2X,
                                               float v2Y,
                                               float v2Z)
        Determine the signed distance of the given point (pointX, pointY, pointZ) to the plane of the triangle specified by its three points (v0X, v0Y, v0Z), (v1X, v1Y, v1Z) and (v2X, v2Y, v2Z).

        If the point lies on the front-facing side of the triangle's plane, that is, if the triangle has counter-clockwise winding order as seen from the point, then this method returns a positive number.

        Parameters:
        pointX - the x coordinate of the point
        pointY - the y coordinate of the point
        pointZ - the z coordinate of the point
        v0X - the x coordinate of the first vertex of the triangle
        v0Y - the y coordinate of the first vertex of the triangle
        v0Z - the z coordinate of the first vertex of the triangle
        v1X - the x coordinate of the second vertex of the triangle
        v1Y - the y coordinate of the second vertex of the triangle
        v1Z - the z coordinate of the second vertex of the triangle
        v2X - the x coordinate of the third vertex of the triangle
        v2Y - the y coordinate of the third vertex of the triangle
        v2Z - the z coordinate of the third vertex of the triangle
        Returns:
        the signed distance between the point and the plane of the triangle
      • intersectRayPlane

        public static float intersectRayPlane​(float originX,
                                              float originY,
                                              float originZ,
                                              float dirX,
                                              float dirY,
                                              float dirZ,
                                              float pointX,
                                              float pointY,
                                              float pointZ,
                                              float normalX,
                                              float normalY,
                                              float normalZ,
                                              float epsilon)
        Test whether the ray with given origin (originX, originY, originZ) and direction (dirX, dirY, dirZ) intersects the plane containing the given point (pointX, pointY, pointZ) and having the normal (normalX, normalY, normalZ), and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point.

        This method returns -1.0 if the ray does not intersect the plane, because it is either parallel to the plane or its direction points away from the plane or the ray's origin is on the negative side of the plane (i.e. the plane's normal points away from the ray's origin).

        Reference: https://www.siggraph.org/

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        dirZ - the z coordinate of the ray's direction
        pointX - the x coordinate of a point on the plane
        pointY - the y coordinate of a point on the plane
        pointZ - the z coordinate of a point on the plane
        normalX - the x coordinate of the plane's normal
        normalY - the y coordinate of the plane's normal
        normalZ - the z coordinate of the plane's normal
        epsilon - some small epsilon for when the ray is parallel to the plane
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if the ray intersects the plane; -1.0 otherwise
      • intersectRayPlane

        public static float intersectRayPlane​(Vector3fc origin,
                                              Vector3fc dir,
                                              Vector3fc point,
                                              Vector3fc normal,
                                              float epsilon)
        Test whether the ray with given origin and direction dir intersects the plane containing the given point and having the given normal, and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point.

        This method returns -1.0 if the ray does not intersect the plane, because it is either parallel to the plane or its direction points away from the plane or the ray's origin is on the negative side of the plane (i.e. the plane's normal points away from the ray's origin).

        Reference: https://www.siggraph.org/

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        point - a point on the plane
        normal - the plane's normal
        epsilon - some small epsilon for when the ray is parallel to the plane
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if the ray intersects the plane; -1.0 otherwise
      • intersectRayPlane

        public static float intersectRayPlane​(Rayf ray,
                                              Planef plane,
                                              float epsilon)
        Test whether the given ray intersects the given plane, and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point.

        This method returns -1.0 if the ray does not intersect the plane, because it is either parallel to the plane or its direction points away from the plane or the ray's origin is on the negative side of the plane (i.e. the plane's normal points away from the ray's origin).

        Reference: https://www.siggraph.org/

        Parameters:
        ray - the ray
        plane - the plane
        epsilon - some small epsilon for when the ray is parallel to the plane
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if the ray intersects the plane; -1.0 otherwise
      • intersectRayPlane

        public static float intersectRayPlane​(float originX,
                                              float originY,
                                              float originZ,
                                              float dirX,
                                              float dirY,
                                              float dirZ,
                                              float a,
                                              float b,
                                              float c,
                                              float d,
                                              float epsilon)
        Test whether the ray with given origin (originX, originY, originZ) and direction (dirX, dirY, dirZ) intersects the plane given as the general plane equation a*x + b*y + c*z + d = 0, and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point.

        This method returns -1.0 if the ray does not intersect the plane, because it is either parallel to the plane or its direction points away from the plane or the ray's origin is on the negative side of the plane (i.e. the plane's normal points away from the ray's origin).

        Reference: https://www.siggraph.org/

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        dirZ - the z coordinate of the ray's direction
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the z factor in the plane equation
        d - the constant in the plane equation
        epsilon - some small epsilon for when the ray is parallel to the plane
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if the ray intersects the plane; -1.0 otherwise
      • testAabSphere

        public static boolean testAabSphere​(float minX,
                                            float minY,
                                            float minZ,
                                            float maxX,
                                            float maxY,
                                            float maxZ,
                                            float centerX,
                                            float centerY,
                                            float centerZ,
                                            float radiusSquared)
        Test whether the axis-aligned box with minimum corner (minX, minY, minZ) and maximum corner (maxX, maxY, maxZ) intersects the sphere with the given center (centerX, centerY, centerZ) and square radius radiusSquared.

        Reference: http://stackoverflow.com

        Parameters:
        minX - the x coordinate of the minimum corner of the axis-aligned box
        minY - the y coordinate of the minimum corner of the axis-aligned box
        minZ - the z coordinate of the minimum corner of the axis-aligned box
        maxX - the x coordinate of the maximum corner of the axis-aligned box
        maxY - the y coordinate of the maximum corner of the axis-aligned box
        maxZ - the z coordinate of the maximum corner of the axis-aligned box
        centerX - the x coordinate of the sphere's center
        centerY - the y coordinate of the sphere's center
        centerZ - the z coordinate of the sphere's center
        radiusSquared - the square of the sphere's radius
        Returns:
        true iff the axis-aligned box intersects the sphere; false otherwise
      • testAabSphere

        public static boolean testAabSphere​(Vector3fc min,
                                            Vector3fc max,
                                            Vector3fc center,
                                            float radiusSquared)
        Test whether the axis-aligned box with minimum corner min and maximum corner max intersects the sphere with the given center and square radius radiusSquared.

        Reference: http://stackoverflow.com

        Parameters:
        min - the minimum corner of the axis-aligned box
        max - the maximum corner of the axis-aligned box
        center - the sphere's center
        radiusSquared - the squared of the sphere's radius
        Returns:
        true iff the axis-aligned box intersects the sphere; false otherwise
      • testAabSphere

        public static boolean testAabSphere​(AABBf aabb,
                                            Spheref sphere)
        Test whether the given axis-aligned box intersects the given sphere.

        Reference: http://stackoverflow.com

        Parameters:
        aabb - the AABB
        sphere - the sphere
        Returns:
        true iff the axis-aligned box intersects the sphere; false otherwise
      • findClosestPointOnPlane

        public static Vector3f findClosestPointOnPlane​(float aX,
                                                       float aY,
                                                       float aZ,
                                                       float nX,
                                                       float nY,
                                                       float nZ,
                                                       float pX,
                                                       float pY,
                                                       float pZ,
                                                       Vector3f result)
        Find the point on the given plane which is closest to the specified point (pX, pY, pZ) and store the result in result.
        Parameters:
        aX - the x coordinate of one point on the plane
        aY - the y coordinate of one point on the plane
        aZ - the z coordinate of one point on the plane
        nX - the x coordinate of the unit normal of the plane
        nY - the y coordinate of the unit normal of the plane
        nZ - the z coordinate of the unit normal of the plane
        pX - the x coordinate of the point
        pY - the y coordinate of the point
        pZ - the z coordinate of the point
        result - will hold the result
        Returns:
        result
      • findClosestPointOnLineSegment

        public static Vector3f findClosestPointOnLineSegment​(float aX,
                                                             float aY,
                                                             float aZ,
                                                             float bX,
                                                             float bY,
                                                             float bZ,
                                                             float pX,
                                                             float pY,
                                                             float pZ,
                                                             Vector3f result)
        Find the point on the given line segment which is closest to the specified point (pX, pY, pZ), and store the result in result.
        Parameters:
        aX - the x coordinate of the first end point of the line segment
        aY - the y coordinate of the first end point of the line segment
        aZ - the z coordinate of the first end point of the line segment
        bX - the x coordinate of the second end point of the line segment
        bY - the y coordinate of the second end point of the line segment
        bZ - the z coordinate of the second end point of the line segment
        pX - the x coordinate of the point
        pY - the y coordinate of the point
        pZ - the z coordinate of the point
        result - will hold the result
        Returns:
        result
      • findClosestPointsLineSegments

        public static float findClosestPointsLineSegments​(float a0X,
                                                          float a0Y,
                                                          float a0Z,
                                                          float a1X,
                                                          float a1Y,
                                                          float a1Z,
                                                          float b0X,
                                                          float b0Y,
                                                          float b0Z,
                                                          float b1X,
                                                          float b1Y,
                                                          float b1Z,
                                                          Vector3f resultA,
                                                          Vector3f resultB)
        Find the closest points on the two line segments, store the point on the first line segment in resultA and the point on the second line segment in resultB, and return the square distance between both points.

        Reference: Book "Real-Time Collision Detection" chapter 5.1.9 "Closest Points of Two Line Segments"

        Parameters:
        a0X - the x coordinate of the first line segment's first end point
        a0Y - the y coordinate of the first line segment's first end point
        a0Z - the z coordinate of the first line segment's first end point
        a1X - the x coordinate of the first line segment's second end point
        a1Y - the y coordinate of the first line segment's second end point
        a1Z - the z coordinate of the first line segment's second end point
        b0X - the x coordinate of the second line segment's first end point
        b0Y - the y coordinate of the second line segment's first end point
        b0Z - the z coordinate of the second line segment's first end point
        b1X - the x coordinate of the second line segment's second end point
        b1Y - the y coordinate of the second line segment's second end point
        b1Z - the z coordinate of the second line segment's second end point
        resultA - will hold the point on the first line segment
        resultB - will hold the point on the second line segment
        Returns:
        the square distance between the two closest points
      • findClosestPointsLineSegmentTriangle

        public static float findClosestPointsLineSegmentTriangle​(float aX,
                                                                 float aY,
                                                                 float aZ,
                                                                 float bX,
                                                                 float bY,
                                                                 float bZ,
                                                                 float v0X,
                                                                 float v0Y,
                                                                 float v0Z,
                                                                 float v1X,
                                                                 float v1Y,
                                                                 float v1Z,
                                                                 float v2X,
                                                                 float v2Y,
                                                                 float v2Z,
                                                                 Vector3f lineSegmentResult,
                                                                 Vector3f triangleResult)
        Find the closest points on a line segment and a triangle.

        Reference: Book "Real-Time Collision Detection" chapter 5.1.10 "Closest Points of a Line Segment and a Triangle"

        Parameters:
        aX - the x coordinate of the line segment's first end point
        aY - the y coordinate of the line segment's first end point
        aZ - the z coordinate of the line segment's first end point
        bX - the x coordinate of the line segment's second end point
        bY - the y coordinate of the line segment's second end point
        bZ - the z coordinate of the line segment's second end point
        v0X - the x coordinate of the triangle's first vertex
        v0Y - the y coordinate of the triangle's first vertex
        v0Z - the z coordinate of the triangle's first vertex
        v1X - the x coordinate of the triangle's second vertex
        v1Y - the y coordinate of the triangle's second vertex
        v1Z - the z coordinate of the triangle's second vertex
        v2X - the x coordinate of the triangle's third vertex
        v2Y - the y coordinate of the triangle's third vertex
        v2Z - the z coordinate of the triangle's third vertex
        lineSegmentResult - will hold the closest point on the line segment
        triangleResult - will hold the closest point on the triangle
        Returns:
        the square distance of the closest points
      • findClosestPointOnTriangle

        public static int findClosestPointOnTriangle​(float v0X,
                                                     float v0Y,
                                                     float v0Z,
                                                     float v1X,
                                                     float v1Y,
                                                     float v1Z,
                                                     float v2X,
                                                     float v2Y,
                                                     float v2Z,
                                                     float pX,
                                                     float pY,
                                                     float pZ,
                                                     Vector3f result)
        Determine the closest point on the triangle with the given vertices (v0X, v0Y, v0Z), (v1X, v1Y, v1Z), (v2X, v2Y, v2Z) between that triangle and the given point (pX, pY, pZ) and store that point into the given result.

        Additionally, this method returns whether the closest point is a vertex (POINT_ON_TRIANGLE_VERTEX_0, POINT_ON_TRIANGLE_VERTEX_1, POINT_ON_TRIANGLE_VERTEX_2) of the triangle, lies on an edge (POINT_ON_TRIANGLE_EDGE_01, POINT_ON_TRIANGLE_EDGE_12, POINT_ON_TRIANGLE_EDGE_20) or on the face of the triangle.

        Reference: Book "Real-Time Collision Detection" chapter 5.1.5 "Closest Point on Triangle to Point"

        Parameters:
        v0X - the x coordinate of the first vertex of the triangle
        v0Y - the y coordinate of the first vertex of the triangle
        v0Z - the z coordinate of the first vertex of the triangle
        v1X - the x coordinate of the second vertex of the triangle
        v1Y - the y coordinate of the second vertex of the triangle
        v1Z - the z coordinate of the second vertex of the triangle
        v2X - the x coordinate of the third vertex of the triangle
        v2Y - the y coordinate of the third vertex of the triangle
        v2Z - the z coordinate of the third vertex of the triangle
        pX - the x coordinate of the point
        pY - the y coordinate of the point
        pZ - the y coordinate of the point
        result - will hold the closest point
        Returns:
        one of POINT_ON_TRIANGLE_VERTEX_0, POINT_ON_TRIANGLE_VERTEX_1, POINT_ON_TRIANGLE_VERTEX_2, POINT_ON_TRIANGLE_EDGE_01, POINT_ON_TRIANGLE_EDGE_12, POINT_ON_TRIANGLE_EDGE_20 or POINT_ON_TRIANGLE_FACE
      • findClosestPointOnRectangle

        public static Vector3f findClosestPointOnRectangle​(float aX,
                                                           float aY,
                                                           float aZ,
                                                           float bX,
                                                           float bY,
                                                           float bZ,
                                                           float cX,
                                                           float cY,
                                                           float cZ,
                                                           float pX,
                                                           float pY,
                                                           float pZ,
                                                           Vector3f res)
        Find the point on a given rectangle, specified via three of its corners, which is closest to the specified point (pX, pY, pZ) and store the result into res.

        Reference: Book "Real-Time Collision Detection" chapter 5.1.4.2 "Closest Point on 3D Rectangle to Point"

        Parameters:
        aX - the x coordinate of the first corner point of the rectangle
        aY - the y coordinate of the first corner point of the rectangle
        aZ - the z coordinate of the first corner point of the rectangle
        bX - the x coordinate of the second corner point of the rectangle
        bY - the y coordinate of the second corner point of the rectangle
        bZ - the z coordinate of the second corner point of the rectangle
        cX - the x coordinate of the third corner point of the rectangle
        cY - the y coordinate of the third corner point of the rectangle
        cZ - the z coordinate of the third corner point of the rectangle
        pX - the x coordinate of the point
        pY - the y coordinate of the point
        pZ - the z coordinate of the point
        res - will hold the result
        Returns:
        res
      • intersectSweptSphereTriangle

        public static int intersectSweptSphereTriangle​(float centerX,
                                                       float centerY,
                                                       float centerZ,
                                                       float radius,
                                                       float velX,
                                                       float velY,
                                                       float velZ,
                                                       float v0X,
                                                       float v0Y,
                                                       float v0Z,
                                                       float v1X,
                                                       float v1Y,
                                                       float v1Z,
                                                       float v2X,
                                                       float v2Y,
                                                       float v2Z,
                                                       float epsilon,
                                                       float maxT,
                                                       Vector4f pointAndTime)
        Determine the point of intersection between a sphere with the given center (centerX, centerY, centerZ) and radius moving with the given velocity (velX, velY, velZ) and the triangle specified via its three vertices (v0X, v0Y, v0Z), (v1X, v1Y, v1Z), (v2X, v2Y, v2Z).

        The vertices of the triangle must be specified in counter-clockwise winding order.

        An intersection is only considered if the time of intersection is smaller than the given maxT value.

        Reference: Improved Collision detection and Response

        Parameters:
        centerX - the x coordinate of the sphere's center
        centerY - the y coordinate of the sphere's center
        centerZ - the z coordinate of the sphere's center
        radius - the radius of the sphere
        velX - the x component of the velocity of the sphere
        velY - the y component of the velocity of the sphere
        velZ - the z component of the velocity of the sphere
        v0X - the x coordinate of the first triangle vertex
        v0Y - the y coordinate of the first triangle vertex
        v0Z - the z coordinate of the first triangle vertex
        v1X - the x coordinate of the second triangle vertex
        v1Y - the y coordinate of the second triangle vertex
        v1Z - the z coordinate of the second triangle vertex
        v2X - the x coordinate of the third triangle vertex
        v2Y - the y coordinate of the third triangle vertex
        v2Z - the z coordinate of the third triangle vertex
        epsilon - a small epsilon when testing spheres that move almost parallel to the triangle
        maxT - the maximum intersection time
        pointAndTime - iff the moving sphere and the triangle intersect, this will hold the point of intersection in the (x, y, z) components and the time of intersection in the w component
        Returns:
        POINT_ON_TRIANGLE_FACE if the intersection point lies on the triangle's face, or POINT_ON_TRIANGLE_VERTEX_0, POINT_ON_TRIANGLE_VERTEX_1 or POINT_ON_TRIANGLE_VERTEX_2 if the intersection point is a vertex, or POINT_ON_TRIANGLE_EDGE_01, POINT_ON_TRIANGLE_EDGE_12 or POINT_ON_TRIANGLE_EDGE_20 if the intersection point lies on an edge; or 0 if no intersection
      • testPointInTriangle

        public static boolean testPointInTriangle​(float pX,
                                                  float pY,
                                                  float pZ,
                                                  float v0X,
                                                  float v0Y,
                                                  float v0Z,
                                                  float v1X,
                                                  float v1Y,
                                                  float v1Z,
                                                  float v2X,
                                                  float v2Y,
                                                  float v2Z)
        Test whether the projection of the given point (pX, pY, pZ) lies inside of the triangle defined by the three vertices (v0X, v0Y, v0Z), (v1X, v1Y, v1Z) and (v2X, v2Y, v2Z).

        Reference: Improved Collision detection and Response

        Parameters:
        pX - the x coordinate of the point to test
        pY - the y coordinate of the point to test
        pZ - the z coordinate of the point to test
        v0X - the x coordinate of the first vertex
        v0Y - the y coordinate of the first vertex
        v0Z - the z coordinate of the first vertex
        v1X - the x coordinate of the second vertex
        v1Y - the y coordinate of the second vertex
        v1Z - the z coordinate of the second vertex
        v2X - the x coordinate of the third vertex
        v2Y - the y coordinate of the third vertex
        v2Z - the z coordinate of the third vertex
        Returns:
        true if the projection of the given point lies inside of the given triangle; false otherwise
      • intersectRaySphere

        public static boolean intersectRaySphere​(float originX,
                                                 float originY,
                                                 float originZ,
                                                 float dirX,
                                                 float dirY,
                                                 float dirZ,
                                                 float centerX,
                                                 float centerY,
                                                 float centerZ,
                                                 float radiusSquared,
                                                 Vector2f result)
        Test whether the given ray with the origin (originX, originY, originZ) and normalized direction (dirX, dirY, dirZ) intersects the given sphere with center (centerX, centerY, centerZ) and square radius radiusSquared, and store the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near and far) of intersections into the given result vector.

        This method returns true for a ray whose origin lies inside the sphere.

        Reference: http://www.scratchapixel.com/

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's normalized direction
        dirY - the y coordinate of the ray's normalized direction
        dirZ - the z coordinate of the ray's normalized direction
        centerX - the x coordinate of the sphere's center
        centerY - the y coordinate of the sphere's center
        centerZ - the z coordinate of the sphere's center
        radiusSquared - the sphere radius squared
        result - a vector that will contain the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near, far) of intersections with the sphere
        Returns:
        true if the ray intersects the sphere; false otherwise
      • intersectRaySphere

        public static boolean intersectRaySphere​(Vector3fc origin,
                                                 Vector3fc dir,
                                                 Vector3fc center,
                                                 float radiusSquared,
                                                 Vector2f result)
        Test whether the ray with the given origin and normalized direction dir intersects the sphere with the given center and square radius radiusSquared, and store the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near and far) of intersections into the given result vector.

        This method returns true for a ray whose origin lies inside the sphere.

        Reference: http://www.scratchapixel.com/

        Parameters:
        origin - the ray's origin
        dir - the ray's normalized direction
        center - the sphere's center
        radiusSquared - the sphere radius squared
        result - a vector that will contain the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near, far) of intersections with the sphere
        Returns:
        true if the ray intersects the sphere; false otherwise
      • intersectRaySphere

        public static boolean intersectRaySphere​(Rayf ray,
                                                 Spheref sphere,
                                                 Vector2f result)
        Test whether the given ray intersects the given sphere, and store the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near and far) of intersections into the given result vector.

        This method returns true for a ray whose origin lies inside the sphere.

        Reference: http://www.scratchapixel.com/

        Parameters:
        ray - the ray
        sphere - the sphere
        result - a vector that will contain the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near, far) of intersections with the sphere
        Returns:
        true if the ray intersects the sphere; false otherwise
      • testRaySphere

        public static boolean testRaySphere​(float originX,
                                            float originY,
                                            float originZ,
                                            float dirX,
                                            float dirY,
                                            float dirZ,
                                            float centerX,
                                            float centerY,
                                            float centerZ,
                                            float radiusSquared)
        Test whether the given ray with the origin (originX, originY, originZ) and normalized direction (dirX, dirY, dirZ) intersects the given sphere with center (centerX, centerY, centerZ) and square radius radiusSquared.

        This method returns true for a ray whose origin lies inside the sphere.

        Reference: http://www.scratchapixel.com/

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's normalized direction
        dirY - the y coordinate of the ray's normalized direction
        dirZ - the z coordinate of the ray's normalized direction
        centerX - the x coordinate of the sphere's center
        centerY - the y coordinate of the sphere's center
        centerZ - the z coordinate of the sphere's center
        radiusSquared - the sphere radius squared
        Returns:
        true if the ray intersects the sphere; false otherwise
      • testRaySphere

        public static boolean testRaySphere​(Vector3fc origin,
                                            Vector3fc dir,
                                            Vector3fc center,
                                            float radiusSquared)
        Test whether the ray with the given origin and normalized direction dir intersects the sphere with the given center and square radius.

        This method returns true for a ray whose origin lies inside the sphere.

        Reference: http://www.scratchapixel.com/

        Parameters:
        origin - the ray's origin
        dir - the ray's normalized direction
        center - the sphere's center
        radiusSquared - the sphere radius squared
        Returns:
        true if the ray intersects the sphere; false otherwise
      • testRaySphere

        public static boolean testRaySphere​(Rayf ray,
                                            Spheref sphere)
        Test whether the given ray intersects the given sphere.

        This method returns true for a ray whose origin lies inside the sphere.

        Reference: http://www.scratchapixel.com/

        Parameters:
        ray - the ray
        sphere - the sphere
        Returns:
        true if the ray intersects the sphere; false otherwise
      • testLineSegmentSphere

        public static boolean testLineSegmentSphere​(float p0X,
                                                    float p0Y,
                                                    float p0Z,
                                                    float p1X,
                                                    float p1Y,
                                                    float p1Z,
                                                    float centerX,
                                                    float centerY,
                                                    float centerZ,
                                                    float radiusSquared)
        Test whether the line segment with the end points (p0X, p0Y, p0Z) and (p1X, p1Y, p1Z) intersects the given sphere with center (centerX, centerY, centerZ) and square radius radiusSquared.

        Reference: http://paulbourke.net/

        Parameters:
        p0X - the x coordinate of the line segment's first end point
        p0Y - the y coordinate of the line segment's first end point
        p0Z - the z coordinate of the line segment's first end point
        p1X - the x coordinate of the line segment's second end point
        p1Y - the y coordinate of the line segment's second end point
        p1Z - the z coordinate of the line segment's second end point
        centerX - the x coordinate of the sphere's center
        centerY - the y coordinate of the sphere's center
        centerZ - the z coordinate of the sphere's center
        radiusSquared - the sphere radius squared
        Returns:
        true if the line segment intersects the sphere; false otherwise
      • testLineSegmentSphere

        public static boolean testLineSegmentSphere​(Vector3fc p0,
                                                    Vector3fc p1,
                                                    Vector3fc center,
                                                    float radiusSquared)
        Test whether the line segment with the end points p0 and p1 intersects the given sphere with center center and square radius radiusSquared.

        Reference: http://paulbourke.net/

        Parameters:
        p0 - the line segment's first end point
        p1 - the line segment's second end point
        center - the sphere's center
        radiusSquared - the sphere radius squared
        Returns:
        true if the line segment intersects the sphere; false otherwise
      • intersectRayAab

        public static boolean intersectRayAab​(float originX,
                                              float originY,
                                              float originZ,
                                              float dirX,
                                              float dirY,
                                              float dirZ,
                                              float minX,
                                              float minY,
                                              float minZ,
                                              float maxX,
                                              float maxY,
                                              float maxZ,
                                              Vector2f result)
        Test whether the given ray with the origin (originX, originY, originZ) and direction (dirX, dirY, dirZ) intersects the axis-aligned box given as its minimum corner (minX, minY, minZ) and maximum corner (maxX, maxY, maxZ), and return the values of the parameter t in the ray equation p(t) = origin + t * dir of the near and far point of intersection.

        This method returns true for a ray whose origin lies inside the axis-aligned box.

        If many boxes need to be tested against the same ray, then the RayAabIntersection class is likely more efficient.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        dirZ - the z coordinate of the ray's direction
        minX - the x coordinate of the minimum corner of the axis-aligned box
        minY - the y coordinate of the minimum corner of the axis-aligned box
        minZ - the z coordinate of the minimum corner of the axis-aligned box
        maxX - the x coordinate of the maximum corner of the axis-aligned box
        maxY - the y coordinate of the maximum corner of the axis-aligned box
        maxZ - the y coordinate of the maximum corner of the axis-aligned box
        result - a vector which will hold the resulting values of the parameter t in the ray equation p(t) = origin + t * dir of the near and far point of intersection iff the ray intersects the axis-aligned box
        Returns:
        true if the given ray intersects the axis-aligned box; false otherwise
        See Also:
        intersectRayAab(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector2f), RayAabIntersection
      • intersectRayAab

        public static boolean intersectRayAab​(Vector3fc origin,
                                              Vector3fc dir,
                                              Vector3fc min,
                                              Vector3fc max,
                                              Vector2f result)
        Test whether the ray with the given origin and direction dir intersects the axis-aligned box specified as its minimum corner min and maximum corner max, and return the values of the parameter t in the ray equation p(t) = origin + t * dir of the near and far point of intersection..

        This method returns true for a ray whose origin lies inside the axis-aligned box.

        If many boxes need to be tested against the same ray, then the RayAabIntersection class is likely more efficient.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        min - the minimum corner of the axis-aligned box
        max - the maximum corner of the axis-aligned box
        result - a vector which will hold the resulting values of the parameter t in the ray equation p(t) = origin + t * dir of the near and far point of intersection iff the ray intersects the axis-aligned box
        Returns:
        true if the given ray intersects the axis-aligned box; false otherwise
        See Also:
        intersectRayAab(float, float, float, float, float, float, float, float, float, float, float, float, Vector2f), RayAabIntersection
      • intersectLineSegmentAab

        public static int intersectLineSegmentAab​(float p0X,
                                                  float p0Y,
                                                  float p0Z,
                                                  float p1X,
                                                  float p1Y,
                                                  float p1Z,
                                                  float minX,
                                                  float minY,
                                                  float minZ,
                                                  float maxX,
                                                  float maxY,
                                                  float maxZ,
                                                  Vector2f result)
        Determine whether the undirected line segment with the end points (p0X, p0Y, p0Z) and (p1X, p1Y, p1Z) intersects the axis-aligned box given as its minimum corner (minX, minY, minZ) and maximum corner (maxX, maxY, maxZ), and return the values of the parameter t in the ray equation p(t) = origin + p0 * (p1 - p0) of the near and far point of intersection.

        This method returns true for a line segment whose either end point lies inside the axis-aligned box.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        p0X - the x coordinate of the line segment's first end point
        p0Y - the y coordinate of the line segment's first end point
        p0Z - the z coordinate of the line segment's first end point
        p1X - the x coordinate of the line segment's second end point
        p1Y - the y coordinate of the line segment's second end point
        p1Z - the z coordinate of the line segment's second end point
        minX - the x coordinate of one corner of the axis-aligned box
        minY - the y coordinate of one corner of the axis-aligned box
        minZ - the z coordinate of one corner of the axis-aligned box
        maxX - the x coordinate of the opposite corner of the axis-aligned box
        maxY - the y coordinate of the opposite corner of the axis-aligned box
        maxZ - the y coordinate of the opposite corner of the axis-aligned box
        result - a vector which will hold the resulting values of the parameter t in the ray equation p(t) = p0 + t * (p1 - p0) of the near and far point of intersection iff the line segment intersects the axis-aligned box
        Returns:
        INSIDE if the line segment lies completely inside of the axis-aligned box; or OUTSIDE if the line segment lies completely outside of the axis-aligned box; or ONE_INTERSECTION if one of the end points of the line segment lies inside of the axis-aligned box; or TWO_INTERSECTION if the line segment intersects two sides of the axis-aligned box or lies on an edge or a side of the box
        See Also:
        intersectLineSegmentAab(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector2f)
      • intersectLineSegmentAab

        public static int intersectLineSegmentAab​(Vector3fc p0,
                                                  Vector3fc p1,
                                                  Vector3fc min,
                                                  Vector3fc max,
                                                  Vector2f result)
        Determine whether the undirected line segment with the end points p0 and p1 intersects the axis-aligned box given as its minimum corner min and maximum corner max, and return the values of the parameter t in the ray equation p(t) = origin + p0 * (p1 - p0) of the near and far point of intersection.

        This method returns true for a line segment whose either end point lies inside the axis-aligned box.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        p0 - the line segment's first end point
        p1 - the line segment's second end point
        min - the minimum corner of the axis-aligned box
        max - the maximum corner of the axis-aligned box
        result - a vector which will hold the resulting values of the parameter t in the ray equation p(t) = p0 + t * (p1 - p0) of the near and far point of intersection iff the line segment intersects the axis-aligned box
        Returns:
        INSIDE if the line segment lies completely inside of the axis-aligned box; or OUTSIDE if the line segment lies completely outside of the axis-aligned box; or ONE_INTERSECTION if one of the end points of the line segment lies inside of the axis-aligned box; or TWO_INTERSECTION if the line segment intersects two sides of the axis-aligned box or lies on an edge or a side of the box
        See Also:
        intersectLineSegmentAab(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector2f)
      • intersectLineSegmentAab

        public static int intersectLineSegmentAab​(LineSegmentf lineSegment,
                                                  AABBf aabb,
                                                  Vector2f result)
        Determine whether the given undirected line segment intersects the given axis-aligned box, and return the values of the parameter t in the ray equation p(t) = origin + p0 * (p1 - p0) of the near and far point of intersection.

        This method returns true for a line segment whose either end point lies inside the axis-aligned box.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        lineSegment - the line segment
        aabb - the AABB
        result - a vector which will hold the resulting values of the parameter t in the ray equation p(t) = p0 + t * (p1 - p0) of the near and far point of intersection iff the line segment intersects the axis-aligned box
        Returns:
        INSIDE if the line segment lies completely inside of the axis-aligned box; or OUTSIDE if the line segment lies completely outside of the axis-aligned box; or ONE_INTERSECTION if one of the end points of the line segment lies inside of the axis-aligned box; or TWO_INTERSECTION if the line segment intersects two sides of the axis-aligned box or lies on an edge or a side of the box
        See Also:
        intersectLineSegmentAab(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector2f)
      • testRayAab

        public static boolean testRayAab​(float originX,
                                         float originY,
                                         float originZ,
                                         float dirX,
                                         float dirY,
                                         float dirZ,
                                         float minX,
                                         float minY,
                                         float minZ,
                                         float maxX,
                                         float maxY,
                                         float maxZ)
        Test whether the given ray with the origin (originX, originY, originZ) and direction (dirX, dirY, dirZ) intersects the axis-aligned box given as its minimum corner (minX, minY, minZ) and maximum corner (maxX, maxY, maxZ).

        This method returns true for a ray whose origin lies inside the axis-aligned box.

        If many boxes need to be tested against the same ray, then the RayAabIntersection class is likely more efficient.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        dirZ - the z coordinate of the ray's direction
        minX - the x coordinate of the minimum corner of the axis-aligned box
        minY - the y coordinate of the minimum corner of the axis-aligned box
        minZ - the z coordinate of the minimum corner of the axis-aligned box
        maxX - the x coordinate of the maximum corner of the axis-aligned box
        maxY - the y coordinate of the maximum corner of the axis-aligned box
        maxZ - the y coordinate of the maximum corner of the axis-aligned box
        Returns:
        true if the given ray intersects the axis-aligned box; false otherwise
        See Also:
        testRayAab(Vector3fc, Vector3fc, Vector3fc, Vector3fc), RayAabIntersection
      • testRayTriangleFront

        public static boolean testRayTriangleFront​(float originX,
                                                   float originY,
                                                   float originZ,
                                                   float dirX,
                                                   float dirY,
                                                   float dirZ,
                                                   float v0X,
                                                   float v0Y,
                                                   float v0Z,
                                                   float v1X,
                                                   float v1Y,
                                                   float v1Z,
                                                   float v2X,
                                                   float v2Y,
                                                   float v2Z,
                                                   float epsilon)
        Test whether the given ray with the origin (originX, originY, originZ) and direction (dirX, dirY, dirZ) intersects the frontface of the triangle consisting of the three vertices (v0X, v0Y, v0Z), (v1X, v1Y, v1Z) and (v2X, v2Y, v2Z).

        This is an implementation of the Fast, Minimum Storage Ray/Triangle Intersection method.

        This test implements backface culling, that is, it will return false when the triangle is in clockwise winding order assuming a right-handed coordinate system when seen along the ray's direction, even if the ray intersects the triangle. This is in compliance with how OpenGL handles backface culling with default frontface/backface settings.

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        dirZ - the z coordinate of the ray's direction
        v0X - the x coordinate of the first vertex
        v0Y - the y coordinate of the first vertex
        v0Z - the z coordinate of the first vertex
        v1X - the x coordinate of the second vertex
        v1Y - the y coordinate of the second vertex
        v1Z - the z coordinate of the second vertex
        v2X - the x coordinate of the third vertex
        v2Y - the y coordinate of the third vertex
        v2Z - the z coordinate of the third vertex
        epsilon - a small epsilon when testing rays that are almost parallel to the triangle
        Returns:
        true if the given ray intersects the frontface of the triangle; false otherwise
        See Also:
        testRayTriangleFront(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector3fc, float)
      • testRayTriangleFront

        public static boolean testRayTriangleFront​(Vector3fc origin,
                                                   Vector3fc dir,
                                                   Vector3fc v0,
                                                   Vector3fc v1,
                                                   Vector3fc v2,
                                                   float epsilon)
        Test whether the ray with the given origin and the given dir intersects the frontface of the triangle consisting of the three vertices v0, v1 and v2.

        This is an implementation of the Fast, Minimum Storage Ray/Triangle Intersection method.

        This test implements backface culling, that is, it will return false when the triangle is in clockwise winding order assuming a right-handed coordinate system when seen along the ray's direction, even if the ray intersects the triangle. This is in compliance with how OpenGL handles backface culling with default frontface/backface settings.

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        v0 - the position of the first vertex
        v1 - the position of the second vertex
        v2 - the position of the third vertex
        epsilon - a small epsilon when testing rays that are almost parallel to the triangle
        Returns:
        true if the given ray intersects the frontface of the triangle; false otherwise
        See Also:
        testRayTriangleFront(float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float)
      • testRayTriangle

        public static boolean testRayTriangle​(float originX,
                                              float originY,
                                              float originZ,
                                              float dirX,
                                              float dirY,
                                              float dirZ,
                                              float v0X,
                                              float v0Y,
                                              float v0Z,
                                              float v1X,
                                              float v1Y,
                                              float v1Z,
                                              float v2X,
                                              float v2Y,
                                              float v2Z,
                                              float epsilon)
        Test whether the given ray with the origin (originX, originY, originZ) and direction (dirX, dirY, dirZ) intersects the triangle consisting of the three vertices (v0X, v0Y, v0Z), (v1X, v1Y, v1Z) and (v2X, v2Y, v2Z).

        This is an implementation of the Fast, Minimum Storage Ray/Triangle Intersection method.

        This test does not take into account the winding order of the triangle, so a ray will intersect a front-facing triangle as well as a back-facing triangle.

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        dirZ - the z coordinate of the ray's direction
        v0X - the x coordinate of the first vertex
        v0Y - the y coordinate of the first vertex
        v0Z - the z coordinate of the first vertex
        v1X - the x coordinate of the second vertex
        v1Y - the y coordinate of the second vertex
        v1Z - the z coordinate of the second vertex
        v2X - the x coordinate of the third vertex
        v2Y - the y coordinate of the third vertex
        v2Z - the z coordinate of the third vertex
        epsilon - a small epsilon when testing rays that are almost parallel to the triangle
        Returns:
        true if the given ray intersects the frontface of the triangle; false otherwise
        See Also:
        testRayTriangle(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector3fc, float)
      • intersectRayTriangleFront

        public static float intersectRayTriangleFront​(float originX,
                                                      float originY,
                                                      float originZ,
                                                      float dirX,
                                                      float dirY,
                                                      float dirZ,
                                                      float v0X,
                                                      float v0Y,
                                                      float v0Z,
                                                      float v1X,
                                                      float v1Y,
                                                      float v1Z,
                                                      float v2X,
                                                      float v2Y,
                                                      float v2Z,
                                                      float epsilon)
        Determine whether the given ray with the origin (originX, originY, originZ) and direction (dirX, dirY, dirZ) intersects the frontface of the triangle consisting of the three vertices (v0X, v0Y, v0Z), (v1X, v1Y, v1Z) and (v2X, v2Y, v2Z) and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the point of intersection.

        This is an implementation of the Fast, Minimum Storage Ray/Triangle Intersection method.

        This test implements backface culling, that is, it will return false when the triangle is in clockwise winding order assuming a right-handed coordinate system when seen along the ray's direction, even if the ray intersects the triangle. This is in compliance with how OpenGL handles backface culling with default frontface/backface settings.

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        dirZ - the z coordinate of the ray's direction
        v0X - the x coordinate of the first vertex
        v0Y - the y coordinate of the first vertex
        v0Z - the z coordinate of the first vertex
        v1X - the x coordinate of the second vertex
        v1Y - the y coordinate of the second vertex
        v1Z - the z coordinate of the second vertex
        v2X - the x coordinate of the third vertex
        v2Y - the y coordinate of the third vertex
        v2Z - the z coordinate of the third vertex
        epsilon - a small epsilon when testing rays that are almost parallel to the triangle
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the point of intersection if the ray intersects the frontface of the triangle; -1.0 otherwise
        See Also:
        testRayTriangleFront(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector3fc, float)
      • intersectRayTriangleFront

        public static float intersectRayTriangleFront​(Vector3fc origin,
                                                      Vector3fc dir,
                                                      Vector3fc v0,
                                                      Vector3fc v1,
                                                      Vector3fc v2,
                                                      float epsilon)
        Determine whether the ray with the given origin and the given dir intersects the frontface of the triangle consisting of the three vertices v0, v1 and v2 and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the point of intersection.

        This is an implementation of the Fast, Minimum Storage Ray/Triangle Intersection method.

        This test implements backface culling, that is, it will return false when the triangle is in clockwise winding order assuming a right-handed coordinate system when seen along the ray's direction, even if the ray intersects the triangle. This is in compliance with how OpenGL handles backface culling with default frontface/backface settings.

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        v0 - the position of the first vertex
        v1 - the position of the second vertex
        v2 - the position of the third vertex
        epsilon - a small epsilon when testing rays that are almost parallel to the triangle
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the point of intersection if the ray intersects the frontface of the triangle; -1.0 otherwise
        See Also:
        intersectRayTriangleFront(float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float)
      • intersectRayTriangle

        public static float intersectRayTriangle​(float originX,
                                                 float originY,
                                                 float originZ,
                                                 float dirX,
                                                 float dirY,
                                                 float dirZ,
                                                 float v0X,
                                                 float v0Y,
                                                 float v0Z,
                                                 float v1X,
                                                 float v1Y,
                                                 float v1Z,
                                                 float v2X,
                                                 float v2Y,
                                                 float v2Z,
                                                 float epsilon)
        Determine whether the given ray with the origin (originX, originY, originZ) and direction (dirX, dirY, dirZ) intersects the triangle consisting of the three vertices (v0X, v0Y, v0Z), (v1X, v1Y, v1Z) and (v2X, v2Y, v2Z) and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the point of intersection.

        This is an implementation of the Fast, Minimum Storage Ray/Triangle Intersection method.

        This test does not take into account the winding order of the triangle, so a ray will intersect a front-facing triangle as well as a back-facing triangle.

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        originZ - the z coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        dirZ - the z coordinate of the ray's direction
        v0X - the x coordinate of the first vertex
        v0Y - the y coordinate of the first vertex
        v0Z - the z coordinate of the first vertex
        v1X - the x coordinate of the second vertex
        v1Y - the y coordinate of the second vertex
        v1Z - the z coordinate of the second vertex
        v2X - the x coordinate of the third vertex
        v2Y - the y coordinate of the third vertex
        v2Z - the z coordinate of the third vertex
        epsilon - a small epsilon when testing rays that are almost parallel to the triangle
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the point of intersection if the ray intersects the triangle; -1.0 otherwise
        See Also:
        testRayTriangle(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector3fc, float)
      • intersectRayTriangle

        public static float intersectRayTriangle​(Vector3fc origin,
                                                 Vector3fc dir,
                                                 Vector3fc v0,
                                                 Vector3fc v1,
                                                 Vector3fc v2,
                                                 float epsilon)
        Determine whether the ray with the given origin and the given dir intersects the triangle consisting of the three vertices v0, v1 and v2 and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the point of intersection.

        This is an implementation of the Fast, Minimum Storage Ray/Triangle Intersection method.

        This test does not take into account the winding order of the triangle, so a ray will intersect a front-facing triangle as well as a back-facing triangle.

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        v0 - the position of the first vertex
        v1 - the position of the second vertex
        v2 - the position of the third vertex
        epsilon - a small epsilon when testing rays that are almost parallel to the triangle
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the point of intersection if the ray intersects the triangle; -1.0 otherwise
        See Also:
        intersectRayTriangle(float, float, float, float, float, float, float, float, float, float, float, float, float, float, float, float)
      • testLineSegmentTriangle

        public static boolean testLineSegmentTriangle​(float p0X,
                                                      float p0Y,
                                                      float p0Z,
                                                      float p1X,
                                                      float p1Y,
                                                      float p1Z,
                                                      float v0X,
                                                      float v0Y,
                                                      float v0Z,
                                                      float v1X,
                                                      float v1Y,
                                                      float v1Z,
                                                      float v2X,
                                                      float v2Y,
                                                      float v2Z,
                                                      float epsilon)
        Test whether the line segment with the end points (p0X, p0Y, p0Z) and (p1X, p1Y, p1Z) intersects the triangle consisting of the three vertices (v0X, v0Y, v0Z), (v1X, v1Y, v1Z) and (v2X, v2Y, v2Z), regardless of the winding order of the triangle or the direction of the line segment between its two end points.

        Reference: Fast, Minimum Storage Ray/Triangle Intersection

        Parameters:
        p0X - the x coordinate of the line segment's first end point
        p0Y - the y coordinate of the line segment's first end point
        p0Z - the z coordinate of the line segment's first end point
        p1X - the x coordinate of the line segment's second end point
        p1Y - the y coordinate of the line segment's second end point
        p1Z - the z coordinate of the line segment's second end point
        v0X - the x coordinate of the first vertex
        v0Y - the y coordinate of the first vertex
        v0Z - the z coordinate of the first vertex
        v1X - the x coordinate of the second vertex
        v1Y - the y coordinate of the second vertex
        v1Z - the z coordinate of the second vertex
        v2X - the x coordinate of the third vertex
        v2Y - the y coordinate of the third vertex
        v2Z - the z coordinate of the third vertex
        epsilon - a small epsilon when testing line segments that are almost parallel to the triangle
        Returns:
        true if the given line segment intersects the triangle; false otherwise
        See Also:
        testLineSegmentTriangle(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector3fc, float)
      • intersectLineSegmentTriangle

        public static boolean intersectLineSegmentTriangle​(float p0X,
                                                           float p0Y,
                                                           float p0Z,
                                                           float p1X,
                                                           float p1Y,
                                                           float p1Z,
                                                           float v0X,
                                                           float v0Y,
                                                           float v0Z,
                                                           float v1X,
                                                           float v1Y,
                                                           float v1Z,
                                                           float v2X,
                                                           float v2Y,
                                                           float v2Z,
                                                           float epsilon,
                                                           Vector3f intersectionPoint)
        Determine whether the line segment with the end points (p0X, p0Y, p0Z) and (p1X, p1Y, p1Z) intersects the triangle consisting of the three vertices (v0X, v0Y, v0Z), (v1X, v1Y, v1Z) and (v2X, v2Y, v2Z), regardless of the winding order of the triangle or the direction of the line segment between its two end points, and return the point of intersection.

        Reference: Fast, Minimum Storage Ray/Triangle Intersection

        Parameters:
        p0X - the x coordinate of the line segment's first end point
        p0Y - the y coordinate of the line segment's first end point
        p0Z - the z coordinate of the line segment's first end point
        p1X - the x coordinate of the line segment's second end point
        p1Y - the y coordinate of the line segment's second end point
        p1Z - the z coordinate of the line segment's second end point
        v0X - the x coordinate of the first vertex
        v0Y - the y coordinate of the first vertex
        v0Z - the z coordinate of the first vertex
        v1X - the x coordinate of the second vertex
        v1Y - the y coordinate of the second vertex
        v1Z - the z coordinate of the second vertex
        v2X - the x coordinate of the third vertex
        v2Y - the y coordinate of the third vertex
        v2Z - the z coordinate of the third vertex
        epsilon - a small epsilon when testing line segments that are almost parallel to the triangle
        intersectionPoint - the point of intersection
        Returns:
        true if the given line segment intersects the triangle; false otherwise
        See Also:
        intersectLineSegmentTriangle(Vector3fc, Vector3fc, Vector3fc, Vector3fc, Vector3fc, float, Vector3f)
      • intersectLineSegmentPlane

        public static boolean intersectLineSegmentPlane​(float p0X,
                                                        float p0Y,
                                                        float p0Z,
                                                        float p1X,
                                                        float p1Y,
                                                        float p1Z,
                                                        float a,
                                                        float b,
                                                        float c,
                                                        float d,
                                                        Vector3f intersectionPoint)
        Determine whether the line segment with the end points (p0X, p0Y, p0Z) and (p1X, p1Y, p1Z) intersects the plane given as the general plane equation a*x + b*y + c*z + d = 0, and return the point of intersection.
        Parameters:
        p0X - the x coordinate of the line segment's first end point
        p0Y - the y coordinate of the line segment's first end point
        p0Z - the z coordinate of the line segment's first end point
        p1X - the x coordinate of the line segment's second end point
        p1Y - the y coordinate of the line segment's second end point
        p1Z - the z coordinate of the line segment's second end point
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the z factor in the plane equation
        d - the constant in the plane equation
        intersectionPoint - the point of intersection
        Returns:
        true if the given line segment intersects the plane; false otherwise
      • testLineCircle

        public static boolean testLineCircle​(float a,
                                             float b,
                                             float c,
                                             float centerX,
                                             float centerY,
                                             float radius)
        Test whether the line with the general line equation a*x + b*y + c = 0 intersects the circle with center (centerX, centerY) and radius.

        Reference: http://math.stackexchange.com

        Parameters:
        a - the x factor in the line equation
        b - the y factor in the line equation
        c - the constant in the line equation
        centerX - the x coordinate of the circle's center
        centerY - the y coordinate of the circle's center
        radius - the radius of the circle
        Returns:
        true iff the line intersects the circle; false otherwise
      • intersectLineCircle

        public static boolean intersectLineCircle​(float a,
                                                  float b,
                                                  float c,
                                                  float centerX,
                                                  float centerY,
                                                  float radius,
                                                  Vector3f intersectionCenterAndHL)
        Test whether the line with the general line equation a*x + b*y + c = 0 intersects the circle with center (centerX, centerY) and radius, and store the center of the line segment of intersection in the (x, y) components of the supplied vector and the half-length of that line segment in the z component.

        Reference: http://math.stackexchange.com

        Parameters:
        a - the x factor in the line equation
        b - the y factor in the line equation
        c - the constant in the line equation
        centerX - the x coordinate of the circle's center
        centerY - the y coordinate of the circle's center
        radius - the radius of the circle
        intersectionCenterAndHL - will hold the center of the line segment of intersection in the (x, y) components and the half-length in the z component
        Returns:
        true iff the line intersects the circle; false otherwise
      • intersectLineCircle

        public static boolean intersectLineCircle​(float x0,
                                                  float y0,
                                                  float x1,
                                                  float y1,
                                                  float centerX,
                                                  float centerY,
                                                  float radius,
                                                  Vector3f intersectionCenterAndHL)
        Test whether the line defined by the two points (x0, y0) and (x1, y1) intersects the circle with center (centerX, centerY) and radius, and store the center of the line segment of intersection in the (x, y) components of the supplied vector and the half-length of that line segment in the z component.

        Reference: http://math.stackexchange.com

        Parameters:
        x0 - the x coordinate of the first point on the line
        y0 - the y coordinate of the first point on the line
        x1 - the x coordinate of the second point on the line
        y1 - the y coordinate of the second point on the line
        centerX - the x coordinate of the circle's center
        centerY - the y coordinate of the circle's center
        radius - the radius of the circle
        intersectionCenterAndHL - will hold the center of the line segment of intersection in the (x, y) components and the half-length in the z component
        Returns:
        true iff the line intersects the circle; false otherwise
      • testAarLine

        public static boolean testAarLine​(float minX,
                                          float minY,
                                          float maxX,
                                          float maxY,
                                          float a,
                                          float b,
                                          float c)
        Test whether the axis-aligned rectangle with minimum corner (minX, minY) and maximum corner (maxX, maxY) intersects the line with the general equation a*x + b*y + c = 0.

        Reference: http://www.lighthouse3d.com ("Geometric Approach - Testing Boxes II")

        Parameters:
        minX - the x coordinate of the minimum corner of the axis-aligned rectangle
        minY - the y coordinate of the minimum corner of the axis-aligned rectangle
        maxX - the x coordinate of the maximum corner of the axis-aligned rectangle
        maxY - the y coordinate of the maximum corner of the axis-aligned rectangle
        a - the x factor in the line equation
        b - the y factor in the line equation
        c - the constant in the plane equation
        Returns:
        true iff the axis-aligned rectangle intersects the line; false otherwise
      • testAarLine

        public static boolean testAarLine​(Vector2fc min,
                                          Vector2fc max,
                                          float a,
                                          float b,
                                          float c)
        Test whether the axis-aligned rectangle with minimum corner min and maximum corner max intersects the line with the general equation a*x + b*y + c = 0.

        Reference: http://www.lighthouse3d.com ("Geometric Approach - Testing Boxes II")

        Parameters:
        min - the minimum corner of the axis-aligned rectangle
        max - the maximum corner of the axis-aligned rectangle
        a - the x factor in the line equation
        b - the y factor in the line equation
        c - the constant in the line equation
        Returns:
        true iff the axis-aligned rectangle intersects the line; false otherwise
      • testAarLine

        public static boolean testAarLine​(float minX,
                                          float minY,
                                          float maxX,
                                          float maxY,
                                          float x0,
                                          float y0,
                                          float x1,
                                          float y1)
        Test whether the axis-aligned rectangle with minimum corner (minX, minY) and maximum corner (maxX, maxY) intersects the line defined by the two points (x0, y0) and (x1, y1).

        Reference: http://www.lighthouse3d.com ("Geometric Approach - Testing Boxes II")

        Parameters:
        minX - the x coordinate of the minimum corner of the axis-aligned rectangle
        minY - the y coordinate of the minimum corner of the axis-aligned rectangle
        maxX - the x coordinate of the maximum corner of the axis-aligned rectangle
        maxY - the y coordinate of the maximum corner of the axis-aligned rectangle
        x0 - the x coordinate of the first point on the line
        y0 - the y coordinate of the first point on the line
        x1 - the x coordinate of the second point on the line
        y1 - the y coordinate of the second point on the line
        Returns:
        true iff the axis-aligned rectangle intersects the line; false otherwise
      • testAarAar

        public static boolean testAarAar​(float minXA,
                                         float minYA,
                                         float maxXA,
                                         float maxYA,
                                         float minXB,
                                         float minYB,
                                         float maxXB,
                                         float maxYB)
        Test whether the axis-aligned rectangle with minimum corner (minXA, minYA) and maximum corner (maxXA, maxYA) intersects the axis-aligned rectangle with minimum corner (minXB, minYB) and maximum corner (maxXB, maxYB).
        Parameters:
        minXA - the x coordinate of the minimum corner of the first axis-aligned rectangle
        minYA - the y coordinate of the minimum corner of the first axis-aligned rectangle
        maxXA - the x coordinate of the maximum corner of the first axis-aligned rectangle
        maxYA - the y coordinate of the maximum corner of the first axis-aligned rectangle
        minXB - the x coordinate of the minimum corner of the second axis-aligned rectangle
        minYB - the y coordinate of the minimum corner of the second axis-aligned rectangle
        maxXB - the x coordinate of the maximum corner of the second axis-aligned rectangle
        maxYB - the y coordinate of the maximum corner of the second axis-aligned rectangle
        Returns:
        true iff both axis-aligned rectangles intersect; false otherwise
      • testAarAar

        public static boolean testAarAar​(Vector2fc minA,
                                         Vector2fc maxA,
                                         Vector2fc minB,
                                         Vector2fc maxB)
        Test whether the axis-aligned rectangle with minimum corner minA and maximum corner maxA intersects the axis-aligned rectangle with minimum corner minB and maximum corner maxB.
        Parameters:
        minA - the minimum corner of the first axis-aligned rectangle
        maxA - the maximum corner of the first axis-aligned rectangle
        minB - the minimum corner of the second axis-aligned rectangle
        maxB - the maximum corner of the second axis-aligned rectangle
        Returns:
        true iff both axis-aligned rectangles intersect; false otherwise
      • testMovingCircleCircle

        public static boolean testMovingCircleCircle​(float aX,
                                                     float aY,
                                                     float maX,
                                                     float maY,
                                                     float aR,
                                                     float bX,
                                                     float bY,
                                                     float bR)
        Test whether a given circle with center (aX, aY) and radius aR and travelled distance vector (maX, maY) intersects a given static circle with center (bX, bY) and radius bR.

        Note that the case of two moving circles can always be reduced to this case by expressing the moved distance of one of the circles relative to the other.

        Reference: https://www.gamasutra.com

        Parameters:
        aX - the x coordinate of the first circle's center
        aY - the y coordinate of the first circle's center
        maX - the x coordinate of the first circle's travelled distance vector
        maY - the y coordinate of the first circle's travelled distance vector
        aR - the radius of the first circle
        bX - the x coordinate of the second circle's center
        bY - the y coordinate of the second circle's center
        bR - the radius of the second circle
        Returns:
        true if both circle intersect; false otherwise
      • testMovingCircleCircle

        public static boolean testMovingCircleCircle​(Vector2f centerA,
                                                     Vector2f moveA,
                                                     float aR,
                                                     Vector2f centerB,
                                                     float bR)
        Test whether a given circle with center centerA and radius aR and travelled distance vector moveA intersects a given static circle with center centerB and radius bR.

        Note that the case of two moving circles can always be reduced to this case by expressing the moved distance of one of the circles relative to the other.

        Reference: https://www.gamasutra.com

        Parameters:
        centerA - the coordinates of the first circle's center
        moveA - the coordinates of the first circle's travelled distance vector
        aR - the radius of the first circle
        centerB - the coordinates of the second circle's center
        bR - the radius of the second circle
        Returns:
        true if both circle intersect; false otherwise
      • intersectCircleCircle

        public static boolean intersectCircleCircle​(float aX,
                                                    float aY,
                                                    float radiusSquaredA,
                                                    float bX,
                                                    float bY,
                                                    float radiusSquaredB,
                                                    Vector3f intersectionCenterAndHL)
        Test whether the one circle with center (aX, aY) and square radius radiusSquaredA intersects the other circle with center (bX, bY) and square radius radiusSquaredB, and store the center of the line segment of intersection in the (x, y) components of the supplied vector and the half-length of that line segment in the z component.

        This method returns false when one circle contains the other circle.

        Reference: http://gamedev.stackexchange.com

        Parameters:
        aX - the x coordinate of the first circle's center
        aY - the y coordinate of the first circle's center
        radiusSquaredA - the square of the first circle's radius
        bX - the x coordinate of the second circle's center
        bY - the y coordinate of the second circle's center
        radiusSquaredB - the square of the second circle's radius
        intersectionCenterAndHL - will hold the center of the circle of intersection in the (x, y, z) components and the radius in the w component
        Returns:
        true iff both circles intersect; false otherwise
      • intersectCircleCircle

        public static boolean intersectCircleCircle​(Vector2fc centerA,
                                                    float radiusSquaredA,
                                                    Vector2fc centerB,
                                                    float radiusSquaredB,
                                                    Vector3f intersectionCenterAndHL)
        Test whether the one circle with center centerA and square radius radiusSquaredA intersects the other circle with center centerB and square radius radiusSquaredB, and store the center of the line segment of intersection in the (x, y) components of the supplied vector and the half-length of that line segment in the z component.

        This method returns false when one circle contains the other circle.

        Reference: http://gamedev.stackexchange.com

        Parameters:
        centerA - the first circle's center
        radiusSquaredA - the square of the first circle's radius
        centerB - the second circle's center
        radiusSquaredB - the square of the second circle's radius
        intersectionCenterAndHL - will hold the center of the line segment of intersection in the (x, y) components and the half-length in the z component
        Returns:
        true iff both circles intersect; false otherwise
      • testCircleCircle

        public static boolean testCircleCircle​(float aX,
                                               float aY,
                                               float rA,
                                               float bX,
                                               float bY,
                                               float rB)
        Test whether the one circle with center (aX, aY) and radius rA intersects the other circle with center (bX, bY) and radius rB.

        This method returns true when one circle contains the other circle.

        Reference: http://math.stackexchange.com/

        Parameters:
        aX - the x coordinate of the first circle's center
        aY - the y coordinate of the first circle's center
        rA - the square of the first circle's radius
        bX - the x coordinate of the second circle's center
        bY - the y coordinate of the second circle's center
        rB - the square of the second circle's radius
        Returns:
        true iff both circles intersect; false otherwise
      • testCircleCircle

        public static boolean testCircleCircle​(Vector2fc centerA,
                                               float radiusSquaredA,
                                               Vector2fc centerB,
                                               float radiusSquaredB)
        Test whether the one circle with center centerA and square radius radiusSquaredA intersects the other circle with center centerB and square radius radiusSquaredB.

        This method returns true when one circle contains the other circle.

        Reference: http://gamedev.stackexchange.com

        Parameters:
        centerA - the first circle's center
        radiusSquaredA - the square of the first circle's radius
        centerB - the second circle's center
        radiusSquaredB - the square of the second circle's radius
        Returns:
        true iff both circles intersect; false otherwise
      • distancePointLine

        public static float distancePointLine​(float pointX,
                                              float pointY,
                                              float a,
                                              float b,
                                              float c)
        Determine the signed distance of the given point (pointX, pointY) to the line specified via its general plane equation a*x + b*y + c = 0.

        Reference: http://mathworld.wolfram.com

        Parameters:
        pointX - the x coordinate of the point
        pointY - the y coordinate of the point
        a - the x factor in the plane equation
        b - the y factor in the plane equation
        c - the constant in the plane equation
        Returns:
        the distance between the point and the line
      • distancePointLine

        public static float distancePointLine​(float pointX,
                                              float pointY,
                                              float x0,
                                              float y0,
                                              float x1,
                                              float y1)
        Determine the signed distance of the given point (pointX, pointY) to the line defined by the two points (x0, y0) and (x1, y1).

        Reference: http://mathworld.wolfram.com

        Parameters:
        pointX - the x coordinate of the point
        pointY - the y coordinate of the point
        x0 - the x coordinate of the first point on the line
        y0 - the y coordinate of the first point on the line
        x1 - the x coordinate of the second point on the line
        y1 - the y coordinate of the second point on the line
        Returns:
        the distance between the point and the line
      • distancePointLine

        public static float distancePointLine​(float pX,
                                              float pY,
                                              float pZ,
                                              float x0,
                                              float y0,
                                              float z0,
                                              float x1,
                                              float y1,
                                              float z1)
        Compute the distance of the given point (pX, pY, pZ) to the line defined by the two points (x0, y0, z0) and (x1, y1, z1).

        Reference: http://mathworld.wolfram.com

        Parameters:
        pX - the x coordinate of the point
        pY - the y coordinate of the point
        pZ - the z coordinate of the point
        x0 - the x coordinate of the first point on the line
        y0 - the y coordinate of the first point on the line
        z0 - the z coordinate of the first point on the line
        x1 - the x coordinate of the second point on the line
        y1 - the y coordinate of the second point on the line
        z1 - the z coordinate of the second point on the line
        Returns:
        the distance between the point and the line
      • intersectRayLine

        public static float intersectRayLine​(float originX,
                                             float originY,
                                             float dirX,
                                             float dirY,
                                             float pointX,
                                             float pointY,
                                             float normalX,
                                             float normalY,
                                             float epsilon)
        Test whether the ray with given origin (originX, originY) and direction (dirX, dirY) intersects the line containing the given point (pointX, pointY) and having the normal (normalX, normalY), and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point.

        This method returns -1.0 if the ray does not intersect the line, because it is either parallel to the line or its direction points away from the line or the ray's origin is on the negative side of the line (i.e. the line's normal points away from the ray's origin).

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        pointX - the x coordinate of a point on the line
        pointY - the y coordinate of a point on the line
        normalX - the x coordinate of the line's normal
        normalY - the y coordinate of the line's normal
        epsilon - some small epsilon for when the ray is parallel to the line
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if the ray intersects the line; -1.0 otherwise
      • intersectRayLine

        public static float intersectRayLine​(Vector2fc origin,
                                             Vector2fc dir,
                                             Vector2fc point,
                                             Vector2fc normal,
                                             float epsilon)
        Test whether the ray with given origin and direction dir intersects the line containing the given point and having the given normal, and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point.

        This method returns -1.0 if the ray does not intersect the line, because it is either parallel to the line or its direction points away from the line or the ray's origin is on the negative side of the line (i.e. the line's normal points away from the ray's origin).

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        point - a point on the line
        normal - the line's normal
        epsilon - some small epsilon for when the ray is parallel to the line
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if the ray intersects the line; -1.0 otherwise
      • intersectRayLineSegment

        public static float intersectRayLineSegment​(float originX,
                                                    float originY,
                                                    float dirX,
                                                    float dirY,
                                                    float aX,
                                                    float aY,
                                                    float bX,
                                                    float bY)
        Determine whether the ray with given origin (originX, originY) and direction (dirX, dirY) intersects the undirected line segment given by the two end points (aX, bY) and (bX, bY), and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if any.

        This method returns -1.0 if the ray does not intersect the line segment.

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        aX - the x coordinate of the line segment's first end point
        aY - the y coordinate of the line segment's first end point
        bX - the x coordinate of the line segment's second end point
        bY - the y coordinate of the line segment's second end point
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if the ray intersects the line segment; -1.0 otherwise
        See Also:
        intersectRayLineSegment(Vector2fc, Vector2fc, Vector2fc, Vector2fc)
      • intersectRayLineSegment

        public static float intersectRayLineSegment​(Vector2fc origin,
                                                    Vector2fc dir,
                                                    Vector2fc a,
                                                    Vector2fc b)
        Determine whether the ray with given origin and direction dir intersects the undirected line segment given by the two end points a and b, and return the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if any.

        This method returns -1.0 if the ray does not intersect the line segment.

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        a - the line segment's first end point
        b - the line segment's second end point
        Returns:
        the value of the parameter t in the ray equation p(t) = origin + t * dir of the intersection point, if the ray intersects the line segment; -1.0 otherwise
        See Also:
        intersectRayLineSegment(float, float, float, float, float, float, float, float)
      • testAarCircle

        public static boolean testAarCircle​(float minX,
                                            float minY,
                                            float maxX,
                                            float maxY,
                                            float centerX,
                                            float centerY,
                                            float radiusSquared)
        Test whether the axis-aligned rectangle with minimum corner (minX, minY) and maximum corner (maxX, maxY) intersects the circle with the given center (centerX, centerY) and square radius radiusSquared.

        Reference: http://stackoverflow.com

        Parameters:
        minX - the x coordinate of the minimum corner of the axis-aligned rectangle
        minY - the y coordinate of the minimum corner of the axis-aligned rectangle
        maxX - the x coordinate of the maximum corner of the axis-aligned rectangle
        maxY - the y coordinate of the maximum corner of the axis-aligned rectangle
        centerX - the x coordinate of the circle's center
        centerY - the y coordinate of the circle's center
        radiusSquared - the square of the circle's radius
        Returns:
        true iff the axis-aligned rectangle intersects the circle; false otherwise
      • testAarCircle

        public static boolean testAarCircle​(Vector2fc min,
                                            Vector2fc max,
                                            Vector2fc center,
                                            float radiusSquared)
        Test whether the axis-aligned rectangle with minimum corner min and maximum corner max intersects the circle with the given center and square radius radiusSquared.

        Reference: http://stackoverflow.com

        Parameters:
        min - the minimum corner of the axis-aligned rectangle
        max - the maximum corner of the axis-aligned rectangle
        center - the circle's center
        radiusSquared - the squared of the circle's radius
        Returns:
        true iff the axis-aligned rectangle intersects the circle; false otherwise
      • intersectRayCircle

        public static boolean intersectRayCircle​(float originX,
                                                 float originY,
                                                 float dirX,
                                                 float dirY,
                                                 float centerX,
                                                 float centerY,
                                                 float radiusSquared,
                                                 Vector2f result)
        Test whether the given ray with the origin (originX, originY) and direction (dirX, dirY) intersects the given circle with center (centerX, centerY) and square radius radiusSquared, and store the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near and far) of intersections into the given result vector.

        This method returns true for a ray whose origin lies inside the circle.

        Reference: http://www.scratchapixel.com/

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        centerX - the x coordinate of the circle's center
        centerY - the y coordinate of the circle's center
        radiusSquared - the circle radius squared
        result - a vector that will contain the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near, far) of intersections with the circle
        Returns:
        true if the ray intersects the circle; false otherwise
      • intersectRayCircle

        public static boolean intersectRayCircle​(Vector2fc origin,
                                                 Vector2fc dir,
                                                 Vector2fc center,
                                                 float radiusSquared,
                                                 Vector2f result)
        Test whether the ray with the given origin and direction dir intersects the circle with the given center and square radius radiusSquared, and store the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near and far) of intersections into the given result vector.

        This method returns true for a ray whose origin lies inside the circle.

        Reference: http://www.scratchapixel.com/

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        center - the circle's center
        radiusSquared - the circle radius squared
        result - a vector that will contain the values of the parameter t in the ray equation p(t) = origin + t * dir for both points (near, far) of intersections with the circle
        Returns:
        true if the ray intersects the circle; false otherwise
      • testRayCircle

        public static boolean testRayCircle​(float originX,
                                            float originY,
                                            float dirX,
                                            float dirY,
                                            float centerX,
                                            float centerY,
                                            float radiusSquared)
        Test whether the given ray with the origin (originX, originY) and direction (dirX, dirY) intersects the given circle with center (centerX, centerY) and square radius radiusSquared.

        This method returns true for a ray whose origin lies inside the circle.

        Reference: http://www.scratchapixel.com/

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        centerX - the x coordinate of the circle's center
        centerY - the y coordinate of the circle's center
        radiusSquared - the circle radius squared
        Returns:
        true if the ray intersects the circle; false otherwise
      • testRayCircle

        public static boolean testRayCircle​(Vector2fc origin,
                                            Vector2fc dir,
                                            Vector2fc center,
                                            float radiusSquared)
        Test whether the ray with the given origin and direction dir intersects the circle with the given center and square radius.

        This method returns true for a ray whose origin lies inside the circle.

        Reference: http://www.scratchapixel.com/

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        center - the circle's center
        radiusSquared - the circle radius squared
        Returns:
        true if the ray intersects the circle; false otherwise
      • intersectRayAar

        public static int intersectRayAar​(float originX,
                                          float originY,
                                          float dirX,
                                          float dirY,
                                          float minX,
                                          float minY,
                                          float maxX,
                                          float maxY,
                                          Vector2f result)
        Determine whether the given ray with the origin (originX, originY) and direction (dirX, dirY) intersects the axis-aligned rectangle given as its minimum corner (minX, minY) and maximum corner (maxX, maxY), and return the values of the parameter t in the ray equation p(t) = origin + t * dir of the near and far point of intersection as well as the side of the axis-aligned rectangle the ray intersects.

        This method also detects an intersection for a ray whose origin lies inside the axis-aligned rectangle.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        minX - the x coordinate of the minimum corner of the axis-aligned rectangle
        minY - the y coordinate of the minimum corner of the axis-aligned rectangle
        maxX - the x coordinate of the maximum corner of the axis-aligned rectangle
        maxY - the y coordinate of the maximum corner of the axis-aligned rectangle
        result - a vector which will hold the values of the parameter t in the ray equation p(t) = origin + t * dir of the near and far point of intersection
        Returns:
        the side on which the near intersection occurred as one of AAR_SIDE_MINX, AAR_SIDE_MINY, AAR_SIDE_MAXX or AAR_SIDE_MAXY; or -1 if the ray does not intersect the axis-aligned rectangle;
        See Also:
        intersectRayAar(Vector2fc, Vector2fc, Vector2fc, Vector2fc, Vector2f)
      • intersectRayAar

        public static int intersectRayAar​(Vector2fc origin,
                                          Vector2fc dir,
                                          Vector2fc min,
                                          Vector2fc max,
                                          Vector2f result)
        Determine whether the given ray with the given origin and direction dir intersects the axis-aligned rectangle given as its minimum corner min and maximum corner max, and return the values of the parameter t in the ray equation p(t) = origin + t * dir of the near and far point of intersection as well as the side of the axis-aligned rectangle the ray intersects.

        This method also detects an intersection for a ray whose origin lies inside the axis-aligned rectangle.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        min - the minimum corner of the axis-aligned rectangle
        max - the maximum corner of the axis-aligned rectangle
        result - a vector which will hold the values of the parameter t in the ray equation p(t) = origin + t * dir of the near and far point of intersection
        Returns:
        the side on which the near intersection occurred as one of AAR_SIDE_MINX, AAR_SIDE_MINY, AAR_SIDE_MAXX or AAR_SIDE_MAXY; or -1 if the ray does not intersect the axis-aligned rectangle;
        See Also:
        intersectRayAar(float, float, float, float, float, float, float, float, Vector2f)
      • intersectLineSegmentAar

        public static int intersectLineSegmentAar​(float p0X,
                                                  float p0Y,
                                                  float p1X,
                                                  float p1Y,
                                                  float minX,
                                                  float minY,
                                                  float maxX,
                                                  float maxY,
                                                  Vector2f result)
        Determine whether the undirected line segment with the end points (p0X, p0Y) and (p1X, p1Y) intersects the axis-aligned rectangle given as its minimum corner (minX, minY) and maximum corner (maxX, maxY), and store the values of the parameter t in the ray equation p(t) = p0 + t * (p1 - p0) of the near and far point of intersection into result.

        This method also detects an intersection of a line segment whose either end point lies inside the axis-aligned rectangle.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        p0X - the x coordinate of the line segment's first end point
        p0Y - the y coordinate of the line segment's first end point
        p1X - the x coordinate of the line segment's second end point
        p1Y - the y coordinate of the line segment's second end point
        minX - the x coordinate of the minimum corner of the axis-aligned rectangle
        minY - the y coordinate of the minimum corner of the axis-aligned rectangle
        maxX - the x coordinate of the maximum corner of the axis-aligned rectangle
        maxY - the y coordinate of the maximum corner of the axis-aligned rectangle
        result - a vector which will hold the values of the parameter t in the ray equation p(t) = p0 + t * (p1 - p0) of the near and far point of intersection
        Returns:
        INSIDE if the line segment lies completely inside of the axis-aligned rectangle; or OUTSIDE if the line segment lies completely outside of the axis-aligned rectangle; or ONE_INTERSECTION if one of the end points of the line segment lies inside of the axis-aligned rectangle; or TWO_INTERSECTION if the line segment intersects two edges of the axis-aligned rectangle or lies on one edge of the rectangle
        See Also:
        intersectLineSegmentAar(Vector2fc, Vector2fc, Vector2fc, Vector2fc, Vector2f)
      • intersectLineSegmentAar

        public static int intersectLineSegmentAar​(Vector2fc p0,
                                                  Vector2fc p1,
                                                  Vector2fc min,
                                                  Vector2fc max,
                                                  Vector2f result)
        Determine whether the undirected line segment with the end points p0 and p1 intersects the axis-aligned rectangle given as its minimum corner min and maximum corner max, and store the values of the parameter t in the ray equation p(t) = p0 + t * (p1 - p0) of the near and far point of intersection into result.

        This method also detects an intersection of a line segment whose either end point lies inside the axis-aligned rectangle.

        Reference: An Efficient and Robust Ray–Box Intersection #see intersectLineSegmentAar(float, float, float, float, float, float, float, float, Vector2f)

        Parameters:
        p0 - the line segment's first end point
        p1 - the line segment's second end point
        min - the minimum corner of the axis-aligned rectangle
        max - the maximum corner of the axis-aligned rectangle
        result - a vector which will hold the values of the parameter t in the ray equation p(t) = p0 + t * (p1 - p0) of the near and far point of intersection
        Returns:
        INSIDE if the line segment lies completely inside of the axis-aligned rectangle; or OUTSIDE if the line segment lies completely outside of the axis-aligned rectangle; or ONE_INTERSECTION if one of the end points of the line segment lies inside of the axis-aligned rectangle; or TWO_INTERSECTION if the line segment intersects two edges of the axis-aligned rectangle
      • testRayAar

        public static boolean testRayAar​(float originX,
                                         float originY,
                                         float dirX,
                                         float dirY,
                                         float minX,
                                         float minY,
                                         float maxX,
                                         float maxY)
        Test whether the given ray with the origin (originX, originY) and direction (dirX, dirY) intersects the given axis-aligned rectangle given as its minimum corner (minX, minY) and maximum corner (maxX, maxY).

        This method returns true for a ray whose origin lies inside the axis-aligned rectangle.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        minX - the x coordinate of the minimum corner of the axis-aligned rectangle
        minY - the y coordinate of the minimum corner of the axis-aligned rectangle
        maxX - the x coordinate of the maximum corner of the axis-aligned rectangle
        maxY - the y coordinate of the maximum corner of the axis-aligned rectangle
        Returns:
        true if the given ray intersects the axis-aligned rectangle; false otherwise
        See Also:
        testRayAar(Vector2fc, Vector2fc, Vector2fc, Vector2fc)
      • testRayAar

        public static boolean testRayAar​(Vector2fc origin,
                                         Vector2fc dir,
                                         Vector2fc min,
                                         Vector2fc max)
        Test whether the ray with the given origin and direction dir intersects the given axis-aligned rectangle specified as its minimum corner min and maximum corner max.

        This method returns true for a ray whose origin lies inside the axis-aligned rectangle.

        Reference: An Efficient and Robust Ray–Box Intersection

        Parameters:
        origin - the ray's origin
        dir - the ray's direction
        min - the minimum corner of the axis-aligned rectangle
        max - the maximum corner of the axis-aligned rectangle
        Returns:
        true if the given ray intersects the axis-aligned rectangle; false otherwise
        See Also:
        testRayAar(float, float, float, float, float, float, float, float)
      • testPointTriangle

        public static boolean testPointTriangle​(float pX,
                                                float pY,
                                                float v0X,
                                                float v0Y,
                                                float v1X,
                                                float v1Y,
                                                float v2X,
                                                float v2Y)
        Test whether the given point (pX, pY) lies inside the triangle with the vertices (v0X, v0Y), (v1X, v1Y), (v2X, v2Y).
        Parameters:
        pX - the x coordinate of the point
        pY - the y coordinate of the point
        v0X - the x coordinate of the first vertex of the triangle
        v0Y - the y coordinate of the first vertex of the triangle
        v1X - the x coordinate of the second vertex of the triangle
        v1Y - the y coordinate of the second vertex of the triangle
        v2X - the x coordinate of the third vertex of the triangle
        v2Y - the y coordinate of the third vertex of the triangle
        Returns:
        true iff the point lies inside the triangle; false otherwise
      • testPointTriangle

        public static boolean testPointTriangle​(Vector2fc point,
                                                Vector2fc v0,
                                                Vector2fc v1,
                                                Vector2fc v2)
        Test whether the given point lies inside the triangle with the vertices v0, v1, v2.
        Parameters:
        v0 - the first vertex of the triangle
        v1 - the second vertex of the triangle
        v2 - the third vertex of the triangle
        point - the point
        Returns:
        true iff the point lies inside the triangle; false otherwise
      • testPointAar

        public static boolean testPointAar​(float pX,
                                           float pY,
                                           float minX,
                                           float minY,
                                           float maxX,
                                           float maxY)
        Test whether the given point (pX, pY) lies inside the axis-aligned rectangle with the minimum corner (minX, minY) and maximum corner (maxX, maxY).
        Parameters:
        pX - the x coordinate of the point
        pY - the y coordinate of the point
        minX - the x coordinate of the minimum corner of the axis-aligned rectangle
        minY - the y coordinate of the minimum corner of the axis-aligned rectangle
        maxX - the x coordinate of the maximum corner of the axis-aligned rectangle
        maxY - the y coordinate of the maximum corner of the axis-aligned rectangle
        Returns:
        true iff the point lies inside the axis-aligned rectangle; false otherwise
      • testPointCircle

        public static boolean testPointCircle​(float pX,
                                              float pY,
                                              float centerX,
                                              float centerY,
                                              float radiusSquared)
        Test whether the point (pX, pY) lies inside the circle with center (centerX, centerY) and square radius radiusSquared.
        Parameters:
        pX - the x coordinate of the point
        pY - the y coordinate of the point
        centerX - the x coordinate of the circle's center
        centerY - the y coordinate of the circle's center
        radiusSquared - the square radius of the circle
        Returns:
        true iff the point lies inside the circle; false otherwise
      • testCircleTriangle

        public static boolean testCircleTriangle​(float centerX,
                                                 float centerY,
                                                 float radiusSquared,
                                                 float v0X,
                                                 float v0Y,
                                                 float v1X,
                                                 float v1Y,
                                                 float v2X,
                                                 float v2Y)
        Test whether the circle with center (centerX, centerY) and square radius radiusSquared intersects the triangle with counter-clockwise vertices (v0X, v0Y), (v1X, v1Y), (v2X, v2Y).

        The vertices of the triangle must be specified in counter-clockwise order.

        Reference: http://www.phatcode.net/

        Parameters:
        centerX - the x coordinate of the circle's center
        centerY - the y coordinate of the circle's center
        radiusSquared - the square radius of the circle
        v0X - the x coordinate of the first vertex of the triangle
        v0Y - the y coordinate of the first vertex of the triangle
        v1X - the x coordinate of the second vertex of the triangle
        v1Y - the y coordinate of the second vertex of the triangle
        v2X - the x coordinate of the third vertex of the triangle
        v2Y - the y coordinate of the third vertex of the triangle
        Returns:
        true iff the circle intersects the triangle; false otherwise
      • testCircleTriangle

        public static boolean testCircleTriangle​(Vector2fc center,
                                                 float radiusSquared,
                                                 Vector2fc v0,
                                                 Vector2fc v1,
                                                 Vector2fc v2)
        Test whether the circle with given center and square radius radiusSquared intersects the triangle with counter-clockwise vertices v0, v1, v2.

        The vertices of the triangle must be specified in counter-clockwise order.

        Reference: http://www.phatcode.net/

        Parameters:
        center - the circle's center
        radiusSquared - the square radius of the circle
        v0 - the first vertex of the triangle
        v1 - the second vertex of the triangle
        v2 - the third vertex of the triangle
        Returns:
        true iff the circle intersects the triangle; false otherwise
      • intersectPolygonRay

        public static int intersectPolygonRay​(float[] verticesXY,
                                              float originX,
                                              float originY,
                                              float dirX,
                                              float dirY,
                                              Vector2f p)
        Determine whether the polygon specified by the given sequence of (x, y) coordinate pairs intersects with the ray with given origin (originX, originY, originZ) and direction (dirX, dirY, dirZ), and store the point of intersection into the given vector p.

        If the polygon intersects the ray, this method returns the index of the polygon edge intersecting the ray, that is, the index of the first vertex of the directed line segment. The second vertex is always that index + 1, modulus the number of polygon vertices.

        Parameters:
        verticesXY - the sequence of (x, y) coordinate pairs of all vertices of the polygon
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        p - will hold the point of intersection
        Returns:
        the index of the first vertex of the polygon edge that intersects the ray; or -1 if the ray does not intersect the polygon
      • intersectPolygonRay

        public static int intersectPolygonRay​(Vector2fc[] vertices,
                                              float originX,
                                              float originY,
                                              float dirX,
                                              float dirY,
                                              Vector2f p)
        Determine whether the polygon specified by the given sequence of vertices intersects with the ray with given origin (originX, originY, originZ) and direction (dirX, dirY, dirZ), and store the point of intersection into the given vector p.

        If the polygon intersects the ray, this method returns the index of the polygon edge intersecting the ray, that is, the index of the first vertex of the directed line segment. The second vertex is always that index + 1, modulus the number of polygon vertices.

        Parameters:
        vertices - the sequence of (x, y) coordinate pairs of all vertices of the polygon
        originX - the x coordinate of the ray's origin
        originY - the y coordinate of the ray's origin
        dirX - the x coordinate of the ray's direction
        dirY - the y coordinate of the ray's direction
        p - will hold the point of intersection
        Returns:
        the index of the first vertex of the polygon edge that intersects the ray; or -1 if the ray does not intersect the polygon
      • intersectLineLine

        public static boolean intersectLineLine​(float ps1x,
                                                float ps1y,
                                                float pe1x,
                                                float pe1y,
                                                float ps2x,
                                                float ps2y,
                                                float pe2x,
                                                float pe2y,
                                                Vector2f p)
        Determine whether the two lines, specified via two points lying on each line, intersect each other, and store the point of intersection into the given vector p.
        Parameters:
        ps1x - the x coordinate of the first point on the first line
        ps1y - the y coordinate of the first point on the first line
        pe1x - the x coordinate of the second point on the first line
        pe1y - the y coordinate of the second point on the first line
        ps2x - the x coordinate of the first point on the second line
        ps2y - the y coordinate of the first point on the second line
        pe2x - the x coordinate of the second point on the second line
        pe2y - the y coordinate of the second point on the second line
        p - will hold the point of intersection
        Returns:
        true iff the two lines intersect; false otherwise
      • testPolygonPolygon

        public static boolean testPolygonPolygon​(Vector2f[] v1s,
                                                 Vector2f[] v2s)
        Test if the two polygons, given via their vertices, intersect.
        Parameters:
        v1s - the vertices of the first polygon
        v2s - the vertices of the second polygon
        Returns:
        true if the polygons intersect; false otherwise