text: //
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  // Copyright (c) 2018-2019 NVIDIA Corporation. All rights reserved.
  
  
  
  #ifndef FLOAT_MATH_LIB_H
  
  #define FLOAT_MATH_LIB_H
  
  #include "ApexUsingNamespace.h"
  #include "PsUserAllocated.h"
  
  // a set of routines that let you do common 3d math
  // operations without any vector, matrix, or quaternion
  // classes or templates.
  //
  // a vector (or point) is a 'float *' to 3 floating point numbers.
  // a matrix is a 'float *' to an array of 16 floating point numbers representing a 4x4 transformation matrix compatible with D3D or OGL
  // a quaternion is a 'float *' to 4 floats representing a quaternion x,y,z,w
  //
  //
  
  
  #include <float.h>
  #include "ApexUsingNamespace.h"
  
  namespace nvidia
  {
  	namespace general_floatmath2
  	{
  		using namespace shdfnd;
  
  enum FM_ClipState
  {
    FMCS_XMIN       = (1<<0),
    FMCS_XMAX       = (1<<1),
    FMCS_YMIN       = (1<<2),
    FMCS_YMAX       = (1<<3),
    FMCS_ZMIN       = (1<<4),
    FMCS_ZMAX       = (1<<5),
  };
  
  enum FM_Axis
  {
    FM_XAXIS   = (1<<0),
    FM_YAXIS   = (1<<1),
    FM_ZAXIS   = (1<<2)
  };
  
  enum LineSegmentType
  {
    LS_START,
    LS_MIDDLE,
    LS_END
  };
  
  
  const float FM_PI = 3.1415926535897932384626433832795028841971693993751f;
  const float FM_DEG_TO_RAD = ((2.0f * FM_PI) / 360.0f);
  const float FM_RAD_TO_DEG = (360.0f / (2.0f * FM_PI));
  
  //***************** Float versions
  //***
  //*** vectors are assumed to be 3 floats or 3 doubles representing X, Y, Z
  //*** quaternions are assumed to be 4 floats or 4 doubles representing X,Y,Z,W
  //*** matrices are assumed to be 16 floats or 16 doubles representing a standard D3D or OpenGL style 4x4 matrix
  //*** bounding volumes are expressed as two sets of 3 floats/double representing bmin(x,y,z) and bmax(x,y,z)
  //*** Plane equations are assumed to be 4 floats or 4 doubles representing Ax,By,Cz,D
  
  FM_Axis fm_getDominantAxis(const float normal[3]);
  FM_Axis fm_getDominantAxis(const double normal[3]);
  
  void fm_decomposeTransform(const float local_transform[16],float trans[3],float rot[4],float scale[3]);
  void fm_decomposeTransform(const double local_transform[16],double trans[3],double rot[4],double scale[3]);
  
  void  fm_multiplyTransform(const float *pA,const float *pB,float *pM);
  void  fm_multiplyTransform(const double *pA,const double *pB,double *pM);
  
  void  fm_inverseTransform(const float matrix[16],float inverse_matrix[16]);
  void  fm_inverseTransform(const double matrix[16],double inverse_matrix[16]);
  
  void  fm_identity(float matrix[16]); // set 4x4 matrix to identity.
  void  fm_identity(double matrix[16]); // set 4x4 matrix to identity.
  
  void  fm_inverseRT(const float matrix[16], const float pos[3], float t[3]); // inverse rotate translate the point.
  void  fm_inverseRT(const double matrix[16],const double pos[3],double t[3]); // inverse rotate translate the point.
  
  void  fm_transform(const float matrix[16], const float pos[3], float t[3]); // rotate and translate this point.
  void  fm_transform(const double matrix[16],const double pos[3],double t[3]); // rotate and translate this point.
  
  float  fm_getDeterminant(const float matrix[16]);
  double fm_getDeterminant(const double matrix[16]);
  
  void fm_getSubMatrix(int32_t ki,int32_t kj,float pDst[16],const float matrix[16]);
  void fm_getSubMatrix(int32_t ki,int32_t kj,double pDst[16],const float matrix[16]);
  
  void  fm_rotate(const float matrix[16],const float pos[3],float t[3]); // only rotate the point by a 4x4 matrix, don't translate.
  void  fm_rotate(const double matri[16],const double pos[3],double t[3]); // only rotate the point by a 4x4 matrix, don't translate.
  
  void  fm_eulerToMatrix(float ax,float ay,float az,float matrix[16]); // convert euler (in radians) to a dest 4x4 matrix (translation set to zero)
  void  fm_eulerToMatrix(double ax,double ay,double az,double matrix[16]); // convert euler (in radians) to a dest 4x4 matrix (translation set to zero)
  
  void  fm_getAABB(uint32_t vcount,const float *points,uint32_t pstride,float bmin[3],float bmax[3]);
  void  fm_getAABB(uint32_t vcount,const double *points,uint32_t pstride,double bmin[3],double bmax[3]);
  
  void  fm_getAABBCenter(const float bmin[3],const float bmax[3],float center[3]);
  void  fm_getAABBCenter(const double bmin[3],const double bmax[3],double center[3]);
  
  void fm_transformAABB(const float bmin[3],const float bmax[3],const float matrix[16],float tbmin[3],float tbmax[3]);
  void fm_transformAABB(const double bmin[3],const double bmax[3],const double matrix[16],double tbmin[3],double tbmax[3]);
  
  void  fm_eulerToQuat(float x,float y,float z,float quat[4]); // convert euler angles to quaternion.
  void  fm_eulerToQuat(double x,double y,double z,double quat[4]); // convert euler angles to quaternion.
  
  void  fm_quatToEuler(const float quat[4],float &ax,float &ay,float &az);
  void  fm_quatToEuler(const double quat[4],double &ax,double &ay,double &az);
  
  void  fm_eulerToQuat(const float euler[3],float quat[4]); // convert euler angles to quaternion. Angles must be radians not degrees!
  void  fm_eulerToQuat(const double euler[3],double quat[4]); // convert euler angles to quaternion.
  
  void  fm_scale(float x,float y,float z,float matrix[16]); // apply scale to the matrix.
  void  fm_scale(double x,double y,double z,double matrix[16]); // apply scale to the matrix.
  
  void  fm_eulerToQuatDX(float x,float y,float z,float quat[4]); // convert euler angles to quaternion using the fucked up DirectX method
  void  fm_eulerToQuatDX(double x,double y,double z,double quat[4]); // convert euler angles to quaternion using the fucked up DirectX method
  
  void  fm_eulerToMatrixDX(float x,float y,float z,float matrix[16]); // convert euler angles to quaternion using the fucked up DirectX method.
  void  fm_eulerToMatrixDX(double x,double y,double z,double matrix[16]); // convert euler angles to quaternion using the fucked up DirectX method.
  
  void  fm_quatToMatrix(const float quat[4],float matrix[16]); // convert quaterinion rotation to matrix, translation set to zero.
  void  fm_quatToMatrix(const double quat[4],double matrix[16]); // convert quaterinion rotation to matrix, translation set to zero.
  
  void  fm_quatRotate(const float quat[4],const float v[3],float r[3]); // rotate a vector directly by a quaternion.
  void  fm_quatRotate(const double quat[4],const double v[3],double r[3]); // rotate a vector directly by a quaternion.
  
  void  fm_getTranslation(const float matrix[16],float t[3]);
  void  fm_getTranslation(const double matrix[16],double t[3]);
  
  void  fm_setTranslation(const float *translation,float matrix[16]);
  void  fm_setTranslation(const double *translation,double matrix[16]);
  
  void  fm_multiplyQuat(const float *qa,const float *qb,float *quat);
  void  fm_multiplyQuat(const double *qa,const double *qb,double *quat);
  
  void  fm_matrixToQuat(const float matrix[16],float quat[4]); // convert the 3x3 portion of a 4x4 matrix into a quaterion as x,y,z,w
  void  fm_matrixToQuat(const double matrix[16],double quat[4]); // convert the 3x3 portion of a 4x4 matrix into a quaterion as x,y,z,w
  
  float fm_sphereVolume(float radius); // return's the volume of a sphere of this radius (4/3 PI * R cubed )
  double fm_sphereVolume(double radius); // return's the volume of a sphere of this radius (4/3 PI * R cubed )
  
  float fm_cylinderVolume(float radius,float h);
  double fm_cylinderVolume(double radius,double h);
  
  float fm_capsuleVolume(float radius,float h);
  double fm_capsuleVolume(double radius,double h);
  
  float fm_distance(const float p1[3],const float p2[3]);
  double fm_distance(const double p1[3],const double p2[3]);
  
  float fm_distanceSquared(const float p1[3],const float p2[3]);
  double fm_distanceSquared(const double p1[3],const double p2[3]);
  
  float fm_distanceSquaredXZ(const float p1[3],const float p2[3]);
  double fm_distanceSquaredXZ(const double p1[3],const double p2[3]);
  
  float fm_computePlane(const float p1[3],const float p2[3],const float p3[3],float *n); // return D
  double fm_computePlane(const double p1[3],const double p2[3],const double p3[3],double *n); // return D
  
  float fm_distToPlane(const float plane[4],const float pos[3]); // computes the distance of this point from the plane.
  double fm_distToPlane(const double plane[4],const double pos[3]); // computes the distance of this point from the plane.
  
  float fm_dot(const float p1[3],const float p2[3]);
  double fm_dot(const double p1[3],const double p2[3]);
  
  void  fm_cross(float cross[3],const float a[3],const float b[3]);
  void  fm_cross(double cross[3],const double a[3],const double b[3]);
  
  void  fm_computeNormalVector(float n[3],const float p1[3],const float p2[3]); // as P2-P1 normalized.
  void  fm_computeNormalVector(double n[3],const double p1[3],const double p2[3]); // as P2-P1 normalized.
  
  bool  fm_computeWindingOrder(const float p1[3],const float p2[3],const float p3[3]); // returns true if the triangle is clockwise.
  bool  fm_computeWindingOrder(const double p1[3],const double p2[3],const double p3[3]); // returns true if the triangle is clockwise.
  
  float  fm_normalize(float n[3]); // normalize this vector and return the distance
  double  fm_normalize(double n[3]); // normalize this vector and return the distance
  
  float  fm_normalizeQuat(float n[4]); // normalize this quat
  double  fm_normalizeQuat(double n[4]); // normalize this quat
  
  void  fm_matrixMultiply(const float A[16],const float B[16],float dest[16]);
  void  fm_matrixMultiply(const double A[16],const double B[16],double dest[16]);
  
  void  fm_composeTransform(const float position[3],const float quat[4],const float scale[3],float matrix[16]);
  void  fm_composeTransform(const double position[3],const double quat[4],const double scale[3],double matrix[16]);
  
  float fm_computeArea(const float p1[3],const float p2[3],const float p3[3]);
  double fm_computeArea(const double p1[3],const double p2[3],const double p3[3]);
  
  void  fm_lerp(const float p1[3],const float p2[3],float dest[3],float lerpValue);
  void  fm_lerp(const double p1[3],const double p2[3],double dest[3],double lerpValue);
  
  bool  fm_insideTriangleXZ(const float test[3],const float p1[3],const float p2[3],const float p3[3]);
  bool  fm_insideTriangleXZ(const double test[3],const double p1[3],const double p2[3],const double p3[3]);
  
  bool  fm_insideAABB(const float pos[3],const float bmin[3],const float bmax[3]);
  bool  fm_insideAABB(const double pos[3],const double bmin[3],const double bmax[3]);
  
  bool  fm_insideAABB(const float obmin[3],const float obmax[3],const float tbmin[3],const float tbmax[3]); // test if bounding box tbmin/tmbax is fully inside obmin/obmax
  bool  fm_insideAABB(const double obmin[3],const double obmax[3],const double tbmin[3],const double tbmax[3]); // test if bounding box tbmin/tmbax is fully inside obmin/obmax
  
  uint32_t fm_clipTestPoint(const float bmin[3],const float bmax[3],const float pos[3]);
  uint32_t fm_clipTestPoint(const double bmin[3],const double bmax[3],const double pos[3]);
  
  uint32_t fm_clipTestPointXZ(const float bmin[3],const float bmax[3],const float pos[3]); // only tests X and Z, not Y
  uint32_t fm_clipTestPointXZ(const double bmin[3],const double bmax[3],const double pos[3]); // only tests X and Z, not Y
  
  
  uint32_t fm_clipTestAABB(const float bmin[3],const float bmax[3],const float p1[3],const float p2[3],const float p3[3],uint32_t &andCode);
  uint32_t fm_clipTestAABB(const double bmin[3],const double bmax[3],const double p1[3],const double p2[3],const double p3[3],uint32_t &andCode);
  
  
  bool     fm_lineTestAABBXZ(const float p1[3],const float p2[3],const float bmin[3],const float bmax[3],float &time);
  bool     fm_lineTestAABBXZ(const double p1[3],const double p2[3],const double bmin[3],const double bmax[3],double &time);
  
  bool     fm_lineTestAABB(const float p1[3],const float p2[3],const float bmin[3],const float bmax[3],float &time);
  bool     fm_lineTestAABB(const double p1[3],const double p2[3],const double bmin[3],const double bmax[3],double &time);
  
  
  void  fm_initMinMax(const float p[3],float bmin[3],float bmax[3]);
  void  fm_initMinMax(const double p[3],double bmin[3],double bmax[3]);
  
  void  fm_initMinMax(float bmin[3],float bmax[3]);
  void  fm_initMinMax(double bmin[3],double bmax[3]);
  
  void  fm_minmax(const float p[3],float bmin[3],float bmax[3]); // accmulate to a min-max value
  void  fm_minmax(const double p[3],double bmin[3],double bmax[3]); // accmulate to a min-max value
  
  
  float fm_solveX(const float plane[4],float y,float z); // solve for X given this plane equation and the other two components.
  double fm_solveX(const double plane[4],double y,double z); // solve for X given this plane equation and the other two components.
  
  float fm_solveY(const float plane[4],float x,float z); // solve for Y given this plane equation and the other two components.
  double fm_solveY(const double plane[4],double x,double z); // solve for Y given this plane equation and the other two components.
  
  float fm_solveZ(const float plane[4],float x,float y); // solve for Z given this plane equation and the other two components.
  double fm_solveZ(const double plane[4],double x,double y); // solve for Z given this plane equation and the other two components.
  
  bool  fm_computeBestFitPlane(uint32_t vcount,     // number of input data points
                       const float *points,     // starting address of points array.
                       uint32_t vstride,    // stride between input points.
                       const float *weights,    // *optional point weighting values.
                       uint32_t wstride,    // weight stride for each vertex.
                       float plane[4]);
  
  bool  fm_computeBestFitPlane(uint32_t vcount,     // number of input data points
                       const double *points,     // starting address of points array.
                       uint32_t vstride,    // stride between input points.
                       const double *weights,    // *optional point weighting values.
                       uint32_t wstride,    // weight stride for each vertex.
                       double plane[4]);
  
  bool  fm_computeCentroid(uint32_t vcount,     // number of input data points
  						 const float *points,     // starting address of points array.
  						 uint32_t vstride,    // stride between input points.
  						 float *center);
  
  bool  fm_computeCentroid(uint32_t vcount,     // number of input data points
  						 const double *points,     // starting address of points array.
  						 uint32_t vstride,    // stride between input points.
  						 double *center);
  
  
  float  fm_computeBestFitAABB(uint32_t vcount,const float *points,uint32_t pstride,float bmin[3],float bmax[3]); // returns the diagonal distance
  double fm_computeBestFitAABB(uint32_t vcount,const double *points,uint32_t pstride,double bmin[3],double bmax[3]); // returns the diagonal distance
  
  float  fm_computeBestFitSphere(uint32_t vcount,const float *points,uint32_t pstride,float center[3]);
  double  fm_computeBestFitSphere(uint32_t vcount,const double *points,uint32_t pstride,double center[3]);
  
  bool fm_lineSphereIntersect(const float center[3],float radius,const float p1[3],const float p2[3],float intersect[3]);
  bool fm_lineSphereIntersect(const double center[3],double radius,const double p1[3],const double p2[3],double intersect[3]);
  
  bool fm_intersectRayAABB(const float bmin[3],const float bmax[3],const float pos[3],const float dir[3],float intersect[3]);
  bool fm_intersectLineSegmentAABB(const float bmin[3],const float bmax[3],const float p1[3],const float p2[3],float intersect[3]);
  
  bool fm_lineIntersectsTriangle(const float rayStart[3],const float rayEnd[3],const float p1[3],const float p2[3],const float p3[3],float sect[3]);
  bool fm_lineIntersectsTriangle(const double rayStart[3],const double rayEnd[3],const double p1[3],const double p2[3],const double p3[3],double sect[3]);
  
  bool fm_rayIntersectsTriangle(const float origin[3],const float dir[3],const float v0[3],const float v1[3],const float v2[3],float &t);
  bool fm_rayIntersectsTriangle(const double origin[3],const double dir[3],const double v0[3],const double v1[3],const double v2[3],double &t);
  
  bool fm_raySphereIntersect(const float center[3],float radius,const float pos[3],const float dir[3],float distance,float intersect[3]);
  bool fm_raySphereIntersect(const double center[3],double radius,const double pos[3],const double dir[3],double distance,double intersect[3]);
  
  void fm_catmullRom(float out_vector[3],const float p1[3],const float p2[3],const float p3[3],const float *p4, const float s);
  void fm_catmullRom(double out_vector[3],const double p1[3],const double p2[3],const double p3[3],const double *p4, const double s);
  
  bool fm_intersectAABB(const float bmin1[3],const float bmax1[3],const float bmin2[3],const float bmax2[3]);
  bool fm_intersectAABB(const double bmin1[3],const double bmax1[3],const double bmin2[3],const double bmax2[3]);
  
  
  // computes the rotation quaternion to go from unit-vector v0 to unit-vector v1
  void fm_rotationArc(const float v0[3],const float v1[3],float quat[4]);
  void fm_rotationArc(const double v0[3],const double v1[3],double quat[4]);
  
  float  fm_distancePointLineSegment(const float Point[3],const float LineStart[3],const float LineEnd[3],float intersection[3],LineSegmentType &type,float epsilon);
  double fm_distancePointLineSegment(const double Point[3],const double LineStart[3],const double LineEnd[3],double intersection[3],LineSegmentType &type,double epsilon);
  
  
  bool fm_colinear(const double p1[3],const double p2[3],const double p3[3],double epsilon=0.999);               // true if these three points in a row are co-linear
  bool fm_colinear(const float  p1[3],const float  p2[3],const float p3[3],float epsilon=0.999f);
  
  bool fm_colinear(const float a1[3],const float a2[3],const float b1[3],const float b2[3],float epsilon=0.999f);  // true if these two line segments are co-linear.
  bool fm_colinear(const double a1[3],const double a2[3],const double b1[3],const double b2[3],double epsilon=0.999);  // true if these two line segments are co-linear.
  
  enum IntersectResult
  {
    IR_DONT_INTERSECT,
    IR_DO_INTERSECT,
    IR_COINCIDENT,
    IR_PARALLEL,
  };
  
  IntersectResult fm_intersectLineSegments2d(const float a1[3], const float a2[3], const float b1[3], const float b2[3], float intersectionPoint[3]);
  IntersectResult fm_intersectLineSegments2d(const double a1[3],const double a2[3],const double b1[3],const double b2[3],double intersectionPoint[3]);
  
  IntersectResult fm_intersectLineSegments2dTime(const float a1[3], const float a2[3], const float b1[3], const float b2[3],float &t1,float &t2);
  IntersectResult fm_intersectLineSegments2dTime(const double a1[3],const double a2[3],const double b1[3],const double b2[3],double &t1,double &t2);
  
  // Plane-Triangle splitting
  
  enum PlaneTriResult
  {
    PTR_ON_PLANE,
    PTR_FRONT,
    PTR_BACK,
    PTR_SPLIT,
  };
  
  PlaneTriResult fm_planeTriIntersection(const float plane[4],    // the plane equation in Ax+By+Cz+D format
                                      const float *triangle, // the source triangle.
                                      uint32_t tstride,  // stride in bytes of the input and output *vertices*
                                      float        epsilon,  // the co-planer epsilon value.
                                      float       *front,    // the triangle in front of the
                                      uint32_t &fcount,  // number of vertices in the 'front' triangle
                                      float       *back,     // the triangle in back of the plane
                                      uint32_t &bcount); // the number of vertices in the 'back' triangle.
  
  
  PlaneTriResult fm_planeTriIntersection(const double plane[4],    // the plane equation in Ax+By+Cz+D format
                                      const double *triangle, // the source triangle.
                                      uint32_t tstride,  // stride in bytes of the input and output *vertices*
                                      double        epsilon,  // the co-planer epsilon value.
                                      double       *front,    // the triangle in front of the
                                      uint32_t &fcount,  // number of vertices in the 'front' triangle
                                      double       *back,     // the triangle in back of the plane
                                      uint32_t &bcount); // the number of vertices in the 'back' triangle.
  
  
  void fm_intersectPointPlane(const float p1[3],const float p2[3],float *split,const float plane[4]);
  void fm_intersectPointPlane(const double p1[3],const double p2[3],double *split,const double plane[4]);
  
  PlaneTriResult fm_getSidePlane(const float p[3],const float plane[4],float epsilon);
  PlaneTriResult fm_getSidePlane(const double p[3],const double plane[4],double epsilon);
  
  
  void fm_computeBestFitOBB(uint32_t vcount,const float *points,uint32_t pstride,float *sides,float matrix[16],bool bruteForce=true);
  void fm_computeBestFitOBB(uint32_t vcount,const double *points,uint32_t pstride,double *sides,double matrix[16],bool bruteForce=true);
  
  void fm_computeBestFitOBB(uint32_t vcount,const float *points,uint32_t pstride,float *sides,float pos[3],float quat[4],bool bruteForce=true);
  void fm_computeBestFitOBB(uint32_t vcount,const double *points,uint32_t pstride,double *sides,double pos[3],double quat[4],bool bruteForce=true);
  
  void fm_computeBestFitABB(uint32_t vcount,const float *points,uint32_t pstride,float *sides,float pos[3]);
  void fm_computeBestFitABB(uint32_t vcount,const double *points,uint32_t pstride,double *sides,double pos[3]);
  
  
  //** Note, if the returned capsule height is less than zero, then you must represent it is a sphere of size radius.
  void fm_computeBestFitCapsule(uint32_t vcount,const float *points,uint32_t pstride,float &radius,float &height,float matrix[16],bool bruteForce=true);
  void fm_computeBestFitCapsule(uint32_t vcount,const double *points,uint32_t pstride,float &radius,float &height,double matrix[16],bool bruteForce=true);
  
  
  void fm_planeToMatrix(const float plane[4],float matrix[16]); // convert a plane equation to a 4x4 rotation matrix.  Reference vector is 0,1,0
  void fm_planeToQuat(const float plane[4],float quat[4],float pos[3]); // convert a plane equation to a quaternion and translation
  
  void fm_planeToMatrix(const double plane[4],double matrix[16]); // convert a plane equation to a 4x4 rotation matrix
  void fm_planeToQuat(const double plane[4],double quat[4],double pos[3]); // convert a plane equation to a quaternion and translation
  
  inline void fm_doubleToFloat3(const double p[3],float t[3]) { t[0] = (float) p[0]; t[1] = (float)p[1]; t[2] = (float)p[2]; };
  inline void fm_floatToDouble3(const float p[3],double t[3]) { t[0] = (double)p[0]; t[1] = (double)p[1]; t[2] = (double)p[2]; };
  
  
  void  fm_eulerMatrix(float ax,float ay,float az,float matrix[16]); // convert euler (in radians) to a dest 4x4 matrix (translation set to zero)
  void  fm_eulerMatrix(double ax,double ay,double az,double matrix[16]); // convert euler (in radians) to a dest 4x4 matrix (translation set to zero)
  
  
  float  fm_computeMeshVolume(const float *vertices,uint32_t tcount,const uint32_t *indices);
  double fm_computeMeshVolume(const double *vertices,uint32_t tcount,const uint32_t *indices);
  
  
  #define FM_DEFAULT_GRANULARITY 0.001f  // 1 millimeter is the default granularity
  
  class fm_VertexIndex
  {
  public:
    virtual uint32_t          getIndex(const float pos[3],bool &newPos) = 0;  // get welded index for this float vector[3]
    virtual uint32_t          getIndex(const double pos[3],bool &newPos) = 0;  // get welded index for this double vector[3]
    virtual const float *   getVerticesFloat(void) const = 0;
    virtual const double *  getVerticesDouble(void) const = 0;
    virtual const float *   getVertexFloat(uint32_t index) const = 0;
    virtual const double *  getVertexDouble(uint32_t index) const = 0;
    virtual uint32_t          getVcount(void) const = 0;
    virtual bool            isDouble(void) const = 0;
    virtual bool            saveAsObj(const char *fname,uint32_t tcount,uint32_t *indices) = 0;
  };
  
  fm_VertexIndex * fm_createVertexIndex(double granularity,bool snapToGrid); // create an indexed vertex system for doubles
  fm_VertexIndex * fm_createVertexIndex(float granularity,bool snapToGrid);  // create an indexed vertext system for floats
  void             fm_releaseVertexIndex(fm_VertexIndex *vindex);
  
  
  
  #if 0 // currently disabled
  
  class fm_LineSegment
  {
  public:
    fm_LineSegment(void)
    {
      mE1 = mE2 = 0;
    }
  
    fm_LineSegment(uint32_t e1,uint32_t e2)
    {
      mE1 = e1;
      mE2 = e2;
    }
  
    uint32_t mE1;
    uint32_t mE2;
  };
  
  
  // LineSweep *only* supports doublees.  As a geometric operation it needs as much precision as possible.
  class fm_LineSweep
  {
  public:
  
   virtual fm_LineSegment * performLineSweep(const fm_LineSegment *segments,
                                     uint32_t icount,
                                     const double *planeEquation,
                                     fm_VertexIndex *pool,
                                     uint32_t &scount) = 0;
  
  
  };
  
  fm_LineSweep * fm_createLineSweep(void);
  void           fm_releaseLineSweep(fm_LineSweep *sweep);
  
  #endif
  
  class fm_Triangulate
  {
  public:
    virtual const double *       triangulate3d(uint32_t pcount,
                                               const double *points,
                                               uint32_t vstride,
                                               uint32_t &tcount,
                                               bool consolidate,
                                               double epsilon) = 0;
  
    virtual const float  *       triangulate3d(uint32_t pcount,
                                               const float  *points,
                                               uint32_t vstride,
                                               uint32_t &tcount,
                                               bool consolidate,
                                               float epsilon) = 0;
  };
  
  fm_Triangulate * fm_createTriangulate(void);
  void             fm_releaseTriangulate(fm_Triangulate *t);
  
  
  const float * fm_getPoint(const float *points,uint32_t pstride,uint32_t index);
  const double * fm_getPoint(const double *points,uint32_t pstride,uint32_t index);
  
  bool   fm_insideTriangle(float Ax, float Ay,float Bx, float By,float Cx, float Cy,float Px, float Py);
  bool   fm_insideTriangle(double Ax, double Ay,double Bx, double By,double Cx, double Cy,double Px, double Py);
  float  fm_areaPolygon2d(uint32_t pcount,const float *points,uint32_t pstride);
  double fm_areaPolygon2d(uint32_t pcount,const double *points,uint32_t pstride);
  
  bool  fm_pointInsidePolygon2d(uint32_t pcount,const float *points,uint32_t pstride,const float *point,uint32_t xindex=0,uint32_t yindex=1);
  bool  fm_pointInsidePolygon2d(uint32_t pcount,const double *points,uint32_t pstride,const double *point,uint32_t xindex=0,uint32_t yindex=1);
  
  uint32_t fm_consolidatePolygon(uint32_t pcount,const float *points,uint32_t pstride,float *dest,float epsilon=0.999999f); // collapses co-linear edges.
  uint32_t fm_consolidatePolygon(uint32_t pcount,const double *points,uint32_t pstride,double *dest,double epsilon=0.999999); // collapses co-linear edges.
  
  
  bool fm_computeSplitPlane(uint32_t vcount,const double *vertices,uint32_t tcount,const uint32_t *indices,double *plane);
  bool fm_computeSplitPlane(uint32_t vcount,const float *vertices,uint32_t tcount,const uint32_t *indices,float *plane);
  
  void fm_nearestPointInTriangle(const float *pos,const float *p1,const float *p2,const float *p3,float *nearest);
  void fm_nearestPointInTriangle(const double *pos,const double *p1,const double *p2,const double *p3,double *nearest);
  
  float  fm_areaTriangle(const float *p1,const float *p2,const float *p3);
  double fm_areaTriangle(const double *p1,const double *p2,const double *p3);
  
  void fm_subtract(const float *A,const float *B,float *diff); // compute A-B and store the result in 'diff'
  void fm_subtract(const double *A,const double *B,double *diff); // compute A-B and store the result in 'diff'
  
  void fm_multiply(float *A,float scaler);
  void fm_multiply(double *A,double scaler);
  
  void fm_add(const float *A,const float *B,float *sum);
  void fm_add(const double *A,const double *B,double *sum);
  
  void fm_copy3(const float *source,float *dest);
  void fm_copy3(const double *source,double *dest);
  
  // re-indexes an indexed triangle mesh but drops unused vertices.  The output_indices can be the same pointer as the input indices.
  // the output_vertices can point to the input vertices if you desire.  The output_vertices buffer should be at least the same size
  // is the input buffer.  The routine returns the new vertex count after re-indexing.
  uint32_t  fm_copyUniqueVertices(uint32_t vcount,const float *input_vertices,float *output_vertices,uint32_t tcount,const uint32_t *input_indices,uint32_t *output_indices);
  uint32_t  fm_copyUniqueVertices(uint32_t vcount,const double *input_vertices,double *output_vertices,uint32_t tcount,const uint32_t *input_indices,uint32_t *output_indices);
  
  bool    fm_isMeshCoplanar(uint32_t tcount,const uint32_t *indices,const float *vertices,bool doubleSided); // returns true if this collection of indexed triangles are co-planar!
  bool    fm_isMeshCoplanar(uint32_t tcount,const uint32_t *indices,const double *vertices,bool doubleSided); // returns true if this collection of indexed triangles are co-planar!
  
  bool    fm_samePlane(const float p1[4],const float p2[4],float normalEpsilon=0.01f,float dEpsilon=0.001f,bool doubleSided=false); // returns true if these two plane equations are identical within an epsilon
  bool    fm_samePlane(const double p1[4],const double p2[4],double normalEpsilon=0.01,double dEpsilon=0.001,bool doubleSided=false);
  
  void    fm_OBBtoAABB(const float obmin[3],const float obmax[3],const float matrix[16],float abmin[3],float abmax[3]);
  
  // a utility class that will tesseleate a mesh.
  class fm_Tesselate
  {
  public:
    virtual const uint32_t * tesselate(fm_VertexIndex *vindex,uint32_t tcount,const uint32_t *indices,float longEdge,uint32_t maxDepth,uint32_t &outcount) = 0;
  };
  
  fm_Tesselate * fm_createTesselate(void);
  void           fm_releaseTesselate(fm_Tesselate *t);
  
  void fm_computeMeanNormals(uint32_t vcount,       // the number of vertices
                             const float *vertices,     // the base address of the vertex position data.
                             uint32_t vstride,      // the stride between position data.
                             float *normals,            // the base address  of the destination for mean vector normals
                             uint32_t nstride,      // the stride between normals
                             uint32_t tcount,       // the number of triangles
                             const uint32_t *indices);     // the triangle indices
  
  void fm_computeMeanNormals(uint32_t vcount,       // the number of vertices
                             const double *vertices,     // the base address of the vertex position data.
                             uint32_t vstride,      // the stride between position data.
                             double *normals,            // the base address  of the destination for mean vector normals
                             uint32_t nstride,      // the stride between normals
                             uint32_t tcount,       // the number of triangles
                             const uint32_t *indices);     // the triangle indices
  
  
  bool fm_isValidTriangle(const float *p1,const float *p2,const float *p3,float epsilon=0.00001f);
  bool fm_isValidTriangle(const double *p1,const double *p2,const double *p3,double epsilon=0.00001f);
  
  }; // end of namespace
  using namespace general_floatmath2;
  };
  
  #endif
  