#ifndef NV_FLOAT_MATH_H #define NV_FLOAT_MATH_H #include "NvUserMemAlloc.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 'NxF32 *' to 3 floating point numbers. // a matrix is a 'NxF32 *' to an array of 16 floating point numbers representing a 4x4 transformation matrix compatible with D3D or OGL // a quaternion is a 'NxF32 *' to 4 floats representing a quaternion x,y,z,w // // /*! ** ** Copyright (c) 2009 by John W. Ratcliff mailto:jratcliffscarab@gmail.com ** ** Portions of this source has been released with the PhysXViewer application, as well as ** Rocket, CreateDynamics, ODF, and as a number of sample code snippets. ** ** If you find this code useful or you are feeling particularily generous I would ** ask that you please go to http://www.amillionpixels.us and make a donation ** to Troy DeMolay. ** ** DeMolay is a youth group for young men between the ages of 12 and 21. ** It teaches strong moral principles, as well as leadership skills and ** public speaking. The donations page uses the 'pay for pixels' paradigm ** where, in this case, a pixel is only a single penny. Donations can be ** made for as small as $4 or as high as a $100 block. Each person who donates ** will get a link to their own site as well as acknowledgement on the ** donations blog located here http://www.amillionpixels.blogspot.com/ ** ** If you wish to contact me you can use the following methods: ** ** Skype ID: jratcliff63367 ** Yahoo: jratcliff63367 ** AOL: jratcliff1961 ** email: jratcliffscarab@gmail.com ** ** ** The MIT license: ** ** Permission is hereby granted, free of charge, to any person obtaining a copy ** of this software and associated documentation files (the "Software"), to deal ** in the Software without restriction, including without limitation the rights ** to use, copy, modify, merge, publish, distribute, sublicense, and/or sell ** copies of the Software, and to permit persons to whom the Software is furnished ** to do so, subject to the following conditions: ** ** The above copyright notice and this permission notice shall be included in all ** copies or substantial portions of the Software. ** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR ** IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, ** FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE ** AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, ** WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN ** CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ #include namespace CONVEX_DECOMPOSITION { 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 NxF32 FM_PI = 3.1415926535897932384626433832795028841971693993751f; const NxF32 FM_DEG_TO_RAD = ((2.0f * FM_PI) / 360.0f); const NxF32 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/NxF64 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 NxF32 normal[3]); FM_Axis fm_getDominantAxis(const NxF64 normal[3]); void fm_decomposeTransform(const NxF32 local_transform[16],NxF32 trans[3],NxF32 rot[4],NxF32 scale[3]); void fm_decomposeTransform(const NxF64 local_transform[16],NxF64 trans[3],NxF64 rot[4],NxF64 scale[3]); void fm_multiplyTransform(const NxF32 *pA,const NxF32 *pB,NxF32 *pM); void fm_multiplyTransform(const NxF64 *pA,const NxF64 *pB,NxF64 *pM); void fm_inverseTransform(const NxF32 matrix[16],NxF32 inverse_matrix[16]); void fm_inverseTransform(const NxF64 matrix[16],NxF64 inverse_matrix[16]); void fm_identity(NxF32 matrix[16]); // set 4x4 matrix to identity. void fm_identity(NxF64 matrix[16]); // set 4x4 matrix to identity. void fm_inverseRT(const NxF32 matrix[16], const NxF32 pos[3], NxF32 t[3]); // inverse rotate translate the point. void fm_inverseRT(const NxF64 matrix[16],const NxF64 pos[3],NxF64 t[3]); // inverse rotate translate the point. void fm_transform(const NxF32 matrix[16], const NxF32 pos[3], NxF32 t[3]); // rotate and translate this point. void fm_transform(const NxF64 matrix[16],const NxF64 pos[3],NxF64 t[3]); // rotate and translate this point. NxF32 fm_getDeterminant(const NxF32 matrix[16]); NxF64 fm_getDeterminant(const NxF64 matrix[16]); void fm_getSubMatrix(NxI32 ki,NxI32 kj,NxF32 pDst[16],const NxF32 matrix[16]); void fm_getSubMatrix(NxI32 ki,NxI32 kj,NxF64 pDst[16],const NxF32 matrix[16]); void fm_rotate(const NxF32 matrix[16],const NxF32 pos[3],NxF32 t[3]); // only rotate the point by a 4x4 matrix, don't translate. void fm_rotate(const NxF64 matri[16],const NxF64 pos[3],NxF64 t[3]); // only rotate the point by a 4x4 matrix, don't translate. void fm_eulerToMatrix(NxF32 ax,NxF32 ay,NxF32 az,NxF32 matrix[16]); // convert euler (in radians) to a dest 4x4 matrix (translation set to zero) void fm_eulerToMatrix(NxF64 ax,NxF64 ay,NxF64 az,NxF64 matrix[16]); // convert euler (in radians) to a dest 4x4 matrix (translation set to zero) void fm_getAABB(NxU32 vcount,const NxF32 *points,NxU32 pstride,NxF32 bmin[3],NxF32 bmax[3]); void fm_getAABB(NxU32 vcount,const NxF64 *points,NxU32 pstride,NxF64 bmin[3],NxF64 bmax[3]); void fm_getAABBCenter(const NxF32 bmin[3],const NxF32 bmax[3],NxF32 center[3]); void fm_getAABBCenter(const NxF64 bmin[3],const NxF64 bmax[3],NxF64 center[3]); void fm_eulerToQuat(NxF32 x,NxF32 y,NxF32 z,NxF32 quat[4]); // convert euler angles to quaternion. void fm_eulerToQuat(NxF64 x,NxF64 y,NxF64 z,NxF64 quat[4]); // convert euler angles to quaternion. void fm_quatToEuler(const NxF32 quat[4],NxF32 &ax,NxF32 &ay,NxF32 &az); void fm_quatToEuler(const NxF64 quat[4],NxF64 &ax,NxF64 &ay,NxF64 &az); void fm_eulerToQuat(const NxF32 euler[3],NxF32 quat[4]); // convert euler angles to quaternion. Angles must be radians not degrees! void fm_eulerToQuat(const NxF64 euler[3],NxF64 quat[4]); // convert euler angles to quaternion. void fm_scale(NxF32 x,NxF32 y,NxF32 z,NxF32 matrix[16]); // apply scale to the matrix. void fm_scale(NxF64 x,NxF64 y,NxF64 z,NxF64 matrix[16]); // apply scale to the matrix. void fm_eulerToQuatDX(NxF32 x,NxF32 y,NxF32 z,NxF32 quat[4]); // convert euler angles to quaternion using the fucked up DirectX method void fm_eulerToQuatDX(NxF64 x,NxF64 y,NxF64 z,NxF64 quat[4]); // convert euler angles to quaternion using the fucked up DirectX method void fm_eulerToMatrixDX(NxF32 x,NxF32 y,NxF32 z,NxF32 matrix[16]); // convert euler angles to quaternion using the fucked up DirectX method. void fm_eulerToMatrixDX(NxF64 x,NxF64 y,NxF64 z,NxF64 matrix[16]); // convert euler angles to quaternion using the fucked up DirectX method. void fm_quatToMatrix(const NxF32 quat[4],NxF32 matrix[16]); // convert quaterinion rotation to matrix, translation set to zero. void fm_quatToMatrix(const NxF64 quat[4],NxF64 matrix[16]); // convert quaterinion rotation to matrix, translation set to zero. void fm_quatRotate(const NxF32 quat[4],const NxF32 v[3],NxF32 r[3]); // rotate a vector directly by a quaternion. void fm_quatRotate(const NxF64 quat[4],const NxF64 v[3],NxF64 r[3]); // rotate a vector directly by a quaternion. void fm_getTranslation(const NxF32 matrix[16],NxF32 t[3]); void fm_getTranslation(const NxF64 matrix[16],NxF64 t[3]); void fm_setTranslation(const NxF32 *translation,NxF32 matrix[16]); void fm_setTranslation(const NxF64 *translation,NxF64 matrix[16]); void fm_multiplyQuat(const NxF32 *qa,const NxF32 *qb,NxF32 *quat); void fm_multiplyQuat(const NxF64 *qa,const NxF64 *qb,NxF64 *quat); void fm_matrixToQuat(const NxF32 matrix[16],NxF32 quat[4]); // convert the 3x3 portion of a 4x4 matrix into a quaterion as x,y,z,w void fm_matrixToQuat(const NxF64 matrix[16],NxF64 quat[4]); // convert the 3x3 portion of a 4x4 matrix into a quaterion as x,y,z,w NxF32 fm_sphereVolume(NxF32 radius); // return's the volume of a sphere of this radius (4/3 PI * R cubed ) NxF64 fm_sphereVolume(NxF64 radius); // return's the volume of a sphere of this radius (4/3 PI * R cubed ) NxF32 fm_cylinderVolume(NxF32 radius,NxF32 h); NxF64 fm_cylinderVolume(NxF64 radius,NxF64 h); NxF32 fm_capsuleVolume(NxF32 radius,NxF32 h); NxF64 fm_capsuleVolume(NxF64 radius,NxF64 h); NxF32 fm_distance(const NxF32 p1[3],const NxF32 p2[3]); NxF64 fm_distance(const NxF64 p1[3],const NxF64 p2[3]); NxF32 fm_distanceSquared(const NxF32 p1[3],const NxF32 p2[3]); NxF64 fm_distanceSquared(const NxF64 p1[3],const NxF64 p2[3]); NxF32 fm_distanceSquaredXZ(const NxF32 p1[3],const NxF32 p2[3]); NxF64 fm_distanceSquaredXZ(const NxF64 p1[3],const NxF64 p2[3]); NxF32 fm_computePlane(const NxF32 p1[3],const NxF32 p2[3],const NxF32 p3[3],NxF32 *n); // return D NxF64 fm_computePlane(const NxF64 p1[3],const NxF64 p2[3],const NxF64 p3[3],NxF64 *n); // return D NxF32 fm_distToPlane(const NxF32 plane[4],const NxF32 pos[3]); // computes the distance of this point from the plane. NxF64 fm_distToPlane(const NxF64 plane[4],const NxF64 pos[3]); // computes the distance of this point from the plane. NxF32 fm_dot(const NxF32 p1[3],const NxF32 p2[3]); NxF64 fm_dot(const NxF64 p1[3],const NxF64 p2[3]); void fm_cross(NxF32 cross[3],const NxF32 a[3],const NxF32 b[3]); void fm_cross(NxF64 cross[3],const NxF64 a[3],const NxF64 b[3]); void fm_computeNormalVector(NxF32 n[3],const NxF32 p1[3],const NxF32 p2[3]); // as P2-P1 normalized. void fm_computeNormalVector(NxF64 n[3],const NxF64 p1[3],const NxF64 p2[3]); // as P2-P1 normalized. bool fm_computeWindingOrder(const NxF32 p1[3],const NxF32 p2[3],const NxF32 p3[3]); // returns true if the triangle is clockwise. bool fm_computeWindingOrder(const NxF64 p1[3],const NxF64 p2[3],const NxF64 p3[3]); // returns true if the triangle is clockwise. NxF32 fm_normalize(NxF32 n[3]); // normalize this vector and return the distance NxF64 fm_normalize(NxF64 n[3]); // normalize this vector and return the distance void fm_matrixMultiply(const NxF32 A[16],const NxF32 B[16],NxF32 dest[16]); void fm_matrixMultiply(const NxF64 A[16],const NxF64 B[16],NxF64 dest[16]); void fm_composeTransform(const NxF32 position[3],const NxF32 quat[4],const NxF32 scale[3],NxF32 matrix[16]); void fm_composeTransform(const NxF64 position[3],const NxF64 quat[4],const NxF64 scale[3],NxF64 matrix[16]); NxF32 fm_computeArea(const NxF32 p1[3],const NxF32 p2[3],const NxF32 p3[3]); NxF64 fm_computeArea(const NxF64 p1[3],const NxF64 p2[3],const NxF64 p3[3]); void fm_lerp(const NxF32 p1[3],const NxF32 p2[3],NxF32 dest[3],NxF32 lerpValue); void fm_lerp(const NxF64 p1[3],const NxF64 p2[3],NxF64 dest[3],NxF64 lerpValue); bool fm_insideTriangleXZ(const NxF32 test[3],const NxF32 p1[3],const NxF32 p2[3],const NxF32 p3[3]); bool fm_insideTriangleXZ(const NxF64 test[3],const NxF64 p1[3],const NxF64 p2[3],const NxF64 p3[3]); bool fm_insideAABB(const NxF32 pos[3],const NxF32 bmin[3],const NxF32 bmax[3]); bool fm_insideAABB(const NxF64 pos[3],const NxF64 bmin[3],const NxF64 bmax[3]); bool fm_insideAABB(const NxF32 obmin[3],const NxF32 obmax[3],const NxF32 tbmin[3],const NxF32 tbmax[3]); // test if bounding box tbmin/tmbax is fully inside obmin/obmax bool fm_insideAABB(const NxF64 obmin[3],const NxF64 obmax[3],const NxF64 tbmin[3],const NxF64 tbmax[3]); // test if bounding box tbmin/tmbax is fully inside obmin/obmax NxU32 fm_clipTestPoint(const NxF32 bmin[3],const NxF32 bmax[3],const NxF32 pos[3]); NxU32 fm_clipTestPoint(const NxF64 bmin[3],const NxF64 bmax[3],const NxF64 pos[3]); NxU32 fm_clipTestPointXZ(const NxF32 bmin[3],const NxF32 bmax[3],const NxF32 pos[3]); // only tests X and Z, not Y NxU32 fm_clipTestPointXZ(const NxF64 bmin[3],const NxF64 bmax[3],const NxF64 pos[3]); // only tests X and Z, not Y NxU32 fm_clipTestAABB(const NxF32 bmin[3],const NxF32 bmax[3],const NxF32 p1[3],const NxF32 p2[3],const NxF32 p3[3],NxU32 &andCode); NxU32 fm_clipTestAABB(const NxF64 bmin[3],const NxF64 bmax[3],const NxF64 p1[3],const NxF64 p2[3],const NxF64 p3[3],NxU32 &andCode); bool fm_lineTestAABBXZ(const NxF32 p1[3],const NxF32 p2[3],const NxF32 bmin[3],const NxF32 bmax[3],NxF32 &time); bool fm_lineTestAABBXZ(const NxF64 p1[3],const NxF64 p2[3],const NxF64 bmin[3],const NxF64 bmax[3],NxF64 &time); bool fm_lineTestAABB(const NxF32 p1[3],const NxF32 p2[3],const NxF32 bmin[3],const NxF32 bmax[3],NxF32 &time); bool fm_lineTestAABB(const NxF64 p1[3],const NxF64 p2[3],const NxF64 bmin[3],const NxF64 bmax[3],NxF64 &time); void fm_initMinMax(const NxF32 p[3],NxF32 bmin[3],NxF32 bmax[3]); void fm_initMinMax(const NxF64 p[3],NxF64 bmin[3],NxF64 bmax[3]); void fm_initMinMax(NxF32 bmin[3],NxF32 bmax[3]); void fm_initMinMax(NxF64 bmin[3],NxF64 bmax[3]); void fm_minmax(const NxF32 p[3],NxF32 bmin[3],NxF32 bmax[3]); // accmulate to a min-max value void fm_minmax(const NxF64 p[3],NxF64 bmin[3],NxF64 bmax[3]); // accmulate to a min-max value NxF32 fm_solveX(const NxF32 plane[4],NxF32 y,NxF32 z); // solve for X given this plane equation and the other two components. NxF64 fm_solveX(const NxF64 plane[4],NxF64 y,NxF64 z); // solve for X given this plane equation and the other two components. NxF32 fm_solveY(const NxF32 plane[4],NxF32 x,NxF32 z); // solve for Y given this plane equation and the other two components. NxF64 fm_solveY(const NxF64 plane[4],NxF64 x,NxF64 z); // solve for Y given this plane equation and the other two components. NxF32 fm_solveZ(const NxF32 plane[4],NxF32 x,NxF32 y); // solve for Z given this plane equation and the other two components. NxF64 fm_solveZ(const NxF64 plane[4],NxF64 x,NxF64 y); // solve for Z given this plane equation and the other two components. bool fm_computeBestFitPlane(NxU32 vcount, // number of input data points const NxF32 *points, // starting address of points array. NxU32 vstride, // stride between input points. const NxF32 *weights, // *optional point weighting values. NxU32 wstride, // weight stride for each vertex. NxF32 plane[4]); bool fm_computeBestFitPlane(NxU32 vcount, // number of input data points const NxF64 *points, // starting address of points array. NxU32 vstride, // stride between input points. const NxF64 *weights, // *optional point weighting values. NxU32 wstride, // weight stride for each vertex. NxF64 plane[4]); NxF32 fm_computeBestFitAABB(NxU32 vcount,const NxF32 *points,NxU32 pstride,NxF32 bmin[3],NxF32 bmax[3]); // returns the diagonal distance NxF64 fm_computeBestFitAABB(NxU32 vcount,const NxF64 *points,NxU32 pstride,NxF64 bmin[3],NxF64 bmax[3]); // returns the diagonal distance NxF32 fm_computeBestFitSphere(NxU32 vcount,const NxF32 *points,NxU32 pstride,NxF32 center[3]); NxF64 fm_computeBestFitSphere(NxU32 vcount,const NxF64 *points,NxU32 pstride,NxF64 center[3]); bool fm_lineSphereIntersect(const NxF32 center[3],NxF32 radius,const NxF32 p1[3],const NxF32 p2[3],NxF32 intersect[3]); bool fm_lineSphereIntersect(const NxF64 center[3],NxF64 radius,const NxF64 p1[3],const NxF64 p2[3],NxF64 intersect[3]); bool fm_intersectRayAABB(const NxF32 bmin[3],const NxF32 bmax[3],const NxF32 pos[3],const NxF32 dir[3],NxF32 intersect[3]); bool fm_intersectLineSegmentAABB(const NxF32 bmin[3],const NxF32 bmax[3],const NxF32 p1[3],const NxF32 p2[3],NxF32 intersect[3]); bool fm_lineIntersectsTriangle(const NxF32 rayStart[3],const NxF32 rayEnd[3],const NxF32 p1[3],const NxF32 p2[3],const NxF32 p3[3],NxF32 sect[3]); bool fm_lineIntersectsTriangle(const NxF64 rayStart[3],const NxF64 rayEnd[3],const NxF64 p1[3],const NxF64 p2[3],const NxF64 p3[3],NxF64 sect[3]); bool fm_rayIntersectsTriangle(const NxF32 origin[3],const NxF32 dir[3],const NxF32 v0[3],const NxF32 v1[3],const NxF32 v2[3],NxF32 &t); bool fm_rayIntersectsTriangle(const NxF64 origin[3],const NxF64 dir[3],const NxF64 v0[3],const NxF64 v1[3],const NxF64 v2[3],NxF64 &t); bool fm_raySphereIntersect(const NxF32 center[3],NxF32 radius,const NxF32 pos[3],const NxF32 dir[3],NxF32 distance,NxF32 intersect[3]); bool fm_raySphereIntersect(const NxF64 center[3],NxF64 radius,const NxF64 pos[3],const NxF64 dir[3],NxF64 distance,NxF64 intersect[3]); void fm_catmullRom(NxF32 out_vector[3],const NxF32 p1[3],const NxF32 p2[3],const NxF32 p3[3],const NxF32 *p4, const NxF32 s); void fm_catmullRom(NxF64 out_vector[3],const NxF64 p1[3],const NxF64 p2[3],const NxF64 p3[3],const NxF64 *p4, const NxF64 s); bool fm_intersectAABB(const NxF32 bmin1[3],const NxF32 bmax1[3],const NxF32 bmin2[3],const NxF32 bmax2[3]); bool fm_intersectAABB(const NxF64 bmin1[3],const NxF64 bmax1[3],const NxF64 bmin2[3],const NxF64 bmax2[3]); // computes the rotation quaternion to go from unit-vector v0 to unit-vector v1 void fm_rotationArc(const NxF32 v0[3],const NxF32 v1[3],NxF32 quat[4]); void fm_rotationArc(const NxF64 v0[3],const NxF64 v1[3],NxF64 quat[4]); NxF32 fm_distancePointLineSegment(const NxF32 Point[3],const NxF32 LineStart[3],const NxF32 LineEnd[3],NxF32 intersection[3],LineSegmentType &type,NxF32 epsilon); NxF64 fm_distancePointLineSegment(const NxF64 Point[3],const NxF64 LineStart[3],const NxF64 LineEnd[3],NxF64 intersection[3],LineSegmentType &type,NxF64 epsilon); bool fm_colinear(const NxF64 p1[3],const NxF64 p2[3],const NxF64 p3[3],NxF64 epsilon=0.999); // true if these three points in a row are co-linear bool fm_colinear(const NxF32 p1[3],const NxF32 p2[3],const NxF32 p3[3],NxF32 epsilon=0.999f); bool fm_colinear(const NxF32 a1[3],const NxF32 a2[3],const NxF32 b1[3],const NxF32 b2[3],NxF32 epsilon=0.999f); // true if these two line segments are co-linear. bool fm_colinear(const NxF64 a1[3],const NxF64 a2[3],const NxF64 b1[3],const NxF64 b2[3],NxF64 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 NxF32 a1[3], const NxF32 a2[3], const NxF32 b1[3], const NxF32 b2[3], NxF32 intersectionPoint[3]); IntersectResult fm_intersectLineSegments2d(const NxF64 a1[3],const NxF64 a2[3],const NxF64 b1[3],const NxF64 b2[3],NxF64 intersectionPoint[3]); IntersectResult fm_intersectLineSegments2dTime(const NxF32 a1[3], const NxF32 a2[3], const NxF32 b1[3], const NxF32 b2[3],NxF32 &t1,NxF32 &t2); IntersectResult fm_intersectLineSegments2dTime(const NxF64 a1[3],const NxF64 a2[3],const NxF64 b1[3],const NxF64 b2[3],NxF64 &t1,NxF64 &t2); // Plane-Triangle splitting enum PlaneTriResult { PTR_ON_PLANE, PTR_FRONT, PTR_BACK, PTR_SPLIT, }; PlaneTriResult fm_planeTriIntersection(const NxF32 plane[4], // the plane equation in Ax+By+Cz+D format const NxF32 *triangle, // the source triangle. NxU32 tstride, // stride in bytes of the input and output *vertices* NxF32 epsilon, // the co-planer epsilon value. NxF32 *front, // the triangle in front of the NxU32 &fcount, // number of vertices in the 'front' triangle NxF32 *back, // the triangle in back of the plane NxU32 &bcount); // the number of vertices in the 'back' triangle. PlaneTriResult fm_planeTriIntersection(const NxF64 plane[4], // the plane equation in Ax+By+Cz+D format const NxF64 *triangle, // the source triangle. NxU32 tstride, // stride in bytes of the input and output *vertices* NxF64 epsilon, // the co-planer epsilon value. NxF64 *front, // the triangle in front of the NxU32 &fcount, // number of vertices in the 'front' triangle NxF64 *back, // the triangle in back of the plane NxU32 &bcount); // the number of vertices in the 'back' triangle. void fm_intersectPointPlane(const NxF32 p1[3],const NxF32 p2[3],NxF32 *split,const NxF32 plane[4]); void fm_intersectPointPlane(const NxF64 p1[3],const NxF64 p2[3],NxF64 *split,const NxF64 plane[4]); PlaneTriResult fm_getSidePlane(const NxF32 p[3],const NxF32 plane[4],NxF32 epsilon); PlaneTriResult fm_getSidePlane(const NxF64 p[3],const NxF64 plane[4],NxF64 epsilon); void fm_computeBestFitOBB(NxU32 vcount,const NxF32 *points,NxU32 pstride,NxF32 *sides,NxF32 matrix[16],bool bruteForce=true); void fm_computeBestFitOBB(NxU32 vcount,const NxF64 *points,NxU32 pstride,NxF64 *sides,NxF64 matrix[16],bool bruteForce=true); void fm_computeBestFitOBB(NxU32 vcount,const NxF32 *points,NxU32 pstride,NxF32 *sides,NxF32 pos[3],NxF32 quat[4],bool bruteForce=true); void fm_computeBestFitOBB(NxU32 vcount,const NxF64 *points,NxU32 pstride,NxF64 *sides,NxF64 pos[3],NxF64 quat[4],bool bruteForce=true); void fm_computeBestFitABB(NxU32 vcount,const NxF32 *points,NxU32 pstride,NxF32 *sides,NxF32 pos[3]); void fm_computeBestFitABB(NxU32 vcount,const NxF64 *points,NxU32 pstride,NxF64 *sides,NxF64 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(NxU32 vcount,const NxF32 *points,NxU32 pstride,NxF32 &radius,NxF32 &height,NxF32 matrix[16],bool bruteForce=true); void fm_computeBestFitCapsule(NxU32 vcount,const NxF64 *points,NxU32 pstride,NxF32 &radius,NxF32 &height,NxF64 matrix[16],bool bruteForce=true); void fm_planeToMatrix(const NxF32 plane[4],NxF32 matrix[16]); // convert a plane equation to a 4x4 rotation matrix. Reference vector is 0,1,0 void fm_planeToQuat(const NxF32 plane[4],NxF32 quat[4],NxF32 pos[3]); // convert a plane equation to a quaternion and translation void fm_planeToMatrix(const NxF64 plane[4],NxF64 matrix[16]); // convert a plane equation to a 4x4 rotation matrix void fm_planeToQuat(const NxF64 plane[4],NxF64 quat[4],NxF64 pos[3]); // convert a plane equation to a quaternion and translation inline void fm_doubleToFloat3(const NxF64 p[3],NxF32 t[3]) { t[0] = (NxF32) p[0]; t[1] = (NxF32)p[1]; t[2] = (NxF32)p[2]; }; inline void fm_floatToDouble3(const NxF32 p[3],NxF64 t[3]) { t[0] = (NxF64)p[0]; t[1] = (NxF64)p[1]; t[2] = (NxF64)p[2]; }; void fm_eulerMatrix(NxF32 ax,NxF32 ay,NxF32 az,NxF32 matrix[16]); // convert euler (in radians) to a dest 4x4 matrix (translation set to zero) void fm_eulerMatrix(NxF64 ax,NxF64 ay,NxF64 az,NxF64 matrix[16]); // convert euler (in radians) to a dest 4x4 matrix (translation set to zero) NxF32 fm_computeMeshVolume(const NxF32 *vertices,NxU32 tcount,const NxU32 *indices); NxF64 fm_computeMeshVolume(const NxF64 *vertices,NxU32 tcount,const NxU32 *indices); #define FM_DEFAULT_GRANULARITY 0.001f // 1 millimeter is the default granularity class fm_VertexIndex { public: virtual NxU32 getIndex(const NxF32 pos[3],bool &newPos) = 0; // get welded index for this NxF32 vector[3] virtual NxU32 getIndex(const NxF64 pos[3],bool &newPos) = 0; // get welded index for this NxF64 vector[3] virtual const NxF32 * getVerticesFloat(void) const = 0; virtual const NxF64 * getVerticesDouble(void) const = 0; virtual const NxF32 * getVertexFloat(NxU32 index) const = 0; virtual const NxF64 * getVertexDouble(NxU32 index) const = 0; virtual NxU32 getVcount(void) const = 0; virtual bool isDouble(void) const = 0; virtual bool saveAsObj(const char *fname,NxU32 tcount,NxU32 *indices) = 0; }; fm_VertexIndex * fm_createVertexIndex(NxF64 granularity,bool snapToGrid); // create an indexed vertex system for doubles fm_VertexIndex * fm_createVertexIndex(NxF32 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(NxU32 e1,NxU32 e2) { mE1 = e1; mE2 = e2; } NxU32 mE1; NxU32 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, NxU32 icount, const NxF64 *planeEquation, fm_VertexIndex *pool, NxU32 &scount) = 0; }; fm_LineSweep * fm_createLineSweep(void); void fm_releaseLineSweep(fm_LineSweep *sweep); #endif class fm_Triangulate { public: virtual const NxF64 * triangulate3d(NxU32 pcount, const NxF64 *points, NxU32 vstride, NxU32 &tcount, bool consolidate, NxF64 epsilon) = 0; virtual const NxF32 * triangulate3d(NxU32 pcount, const NxF32 *points, NxU32 vstride, NxU32 &tcount, bool consolidate, NxF32 epsilon) = 0; }; fm_Triangulate * fm_createTriangulate(void); void fm_releaseTriangulate(fm_Triangulate *t); const NxF32 * fm_getPoint(const NxF32 *points,NxU32 pstride,NxU32 index); const NxF64 * fm_getPoint(const NxF64 *points,NxU32 pstride,NxU32 index); bool fm_insideTriangle(NxF32 Ax, NxF32 Ay,NxF32 Bx, NxF32 By,NxF32 Cx, NxF32 Cy,NxF32 Px, NxF32 Py); bool fm_insideTriangle(NxF64 Ax, NxF64 Ay,NxF64 Bx, NxF64 By,NxF64 Cx, NxF64 Cy,NxF64 Px, NxF64 Py); NxF32 fm_areaPolygon2d(NxU32 pcount,const NxF32 *points,NxU32 pstride); NxF64 fm_areaPolygon2d(NxU32 pcount,const NxF64 *points,NxU32 pstride); bool fm_pointInsidePolygon2d(NxU32 pcount,const NxF32 *points,NxU32 pstride,const NxF32 *point,NxU32 xindex=0,NxU32 yindex=1); bool fm_pointInsidePolygon2d(NxU32 pcount,const NxF64 *points,NxU32 pstride,const NxF64 *point,NxU32 xindex=0,NxU32 yindex=1); NxU32 fm_consolidatePolygon(NxU32 pcount,const NxF32 *points,NxU32 pstride,NxF32 *dest,NxF32 epsilon=0.999999f); // collapses co-linear edges. NxU32 fm_consolidatePolygon(NxU32 pcount,const NxF64 *points,NxU32 pstride,NxF64 *dest,NxF64 epsilon=0.999999); // collapses co-linear edges. bool fm_computeSplitPlane(NxU32 vcount,const NxF64 *vertices,NxU32 tcount,const NxU32 *indices,NxF64 *plane); bool fm_computeSplitPlane(NxU32 vcount,const NxF32 *vertices,NxU32 tcount,const NxU32 *indices,NxF32 *plane); void fm_nearestPointInTriangle(const NxF32 *pos,const NxF32 *p1,const NxF32 *p2,const NxF32 *p3,NxF32 *nearest); void fm_nearestPointInTriangle(const NxF64 *pos,const NxF64 *p1,const NxF64 *p2,const NxF64 *p3,NxF64 *nearest); NxF32 fm_areaTriangle(const NxF32 *p1,const NxF32 *p2,const NxF32 *p3); NxF64 fm_areaTriangle(const NxF64 *p1,const NxF64 *p2,const NxF64 *p3); void fm_subtract(const NxF32 *A,const NxF32 *B,NxF32 *diff); // compute A-B and store the result in 'diff' void fm_subtract(const NxF64 *A,const NxF64 *B,NxF64 *diff); // compute A-B and store the result in 'diff' void fm_multiply(NxF32 *A,NxF32 scaler); void fm_multiply(NxF64 *A,NxF64 scaler); void fm_add(const NxF32 *A,const NxF32 *B,NxF32 *sum); void fm_add(const NxF64 *A,const NxF64 *B,NxF64 *sum); void fm_copy3(const NxF32 *source,NxF32 *dest); void fm_copy3(const NxF64 *source,NxF64 *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. NxU32 fm_copyUniqueVertices(NxU32 vcount,const NxF32 *input_vertices,NxF32 *output_vertices,NxU32 tcount,const NxU32 *input_indices,NxU32 *output_indices); NxU32 fm_copyUniqueVertices(NxU32 vcount,const NxF64 *input_vertices,NxF64 *output_vertices,NxU32 tcount,const NxU32 *input_indices,NxU32 *output_indices); bool fm_isMeshCoplanar(NxU32 tcount,const NxU32 *indices,const NxF32 *vertices,bool doubleSided); // returns true if this collection of indexed triangles are co-planar! bool fm_isMeshCoplanar(NxU32 tcount,const NxU32 *indices,const NxF64 *vertices,bool doubleSided); // returns true if this collection of indexed triangles are co-planar! bool fm_samePlane(const NxF32 p1[4],const NxF32 p2[4],NxF32 normalEpsilon=0.01f,NxF32 dEpsilon=0.001f,bool doubleSided=false); // returns true if these two plane equations are identical within an epsilon bool fm_samePlane(const NxF64 p1[4],const NxF64 p2[4],NxF64 normalEpsilon=0.01,NxF64 dEpsilon=0.001,bool doubleSided=false); void fm_OBBtoAABB(const NxF32 obmin[3],const NxF32 obmax[3],const NxF32 matrix[16],NxF32 abmin[3],NxF32 abmax[3]); // a utility class that will tesseleate a mesh. class fm_Tesselate { public: virtual const NxU32 * tesselate(fm_VertexIndex *vindex,NxU32 tcount,const NxU32 *indices,NxF32 longEdge,NxU32 maxDepth,NxU32 &outcount) = 0; }; fm_Tesselate * fm_createTesselate(void); void fm_releaseTesselate(fm_Tesselate *t); void fm_computeMeanNormals(NxU32 vcount, // the number of vertices const NxF32 *vertices, // the base address of the vertex position data. NxU32 vstride, // the stride between position data. NxF32 *normals, // the base address of the destination for mean vector normals NxU32 nstride, // the stride between normals NxU32 tcount, // the number of triangles const NxU32 *indices); // the triangle indices void fm_computeMeanNormals(NxU32 vcount, // the number of vertices const NxF64 *vertices, // the base address of the vertex position data. NxU32 vstride, // the stride between position data. NxF64 *normals, // the base address of the destination for mean vector normals NxU32 nstride, // the stride between normals NxU32 tcount, // the number of triangles const NxU32 *indices); // the triangle indices bool fm_isValidTriangle(const NxF32 *p1,const NxF32 *p2,const NxF32 *p3,NxF32 epsilon=0.00001f); bool fm_isValidTriangle(const NxF64 *p1,const NxF64 *p2,const NxF64 *p3,NxF64 epsilon=0.00001f); }; // end of namespace #endif