// Math3d.h // Header file for the Math3d library. The C-Runtime has math.h, this file and the // accompanying math.c are meant to suppliment math.h by adding geometry/math routines // useful for graphics, simulation, and physics applications (3D stuff). // Richard S. Wright Jr. #ifndef _MATH3D_LIBRARY__ #define _MATH3D_LIBRARY__ #include #include /////////////////////////////////////////////////////////////////////////////// // Data structures and containers // Much thought went into how these are declared. Many libraries declare these // as structures with x, y, z data members. However structure alignment issues // could limit the portability of code based on such structures, or the binary // compatibility of data files (more likely) that contain such structures across // compilers/platforms. Arrays are always tightly packed, and are more efficient // for moving blocks of data around (usually). typedef float M3DVector3f[3]; // Vector of three floats (x, y, z) typedef double M3DVector3d[3]; // Vector of three doubles (x, y, z) typedef float M3DVector4f[4]; // Lesser used... Do we really need these? typedef double M3DVector4d[4]; // Yes, occasionaly typedef float M3DVector2f[2]; // 3D points = 3D Vectors, but we need a typedef double M3DVector2d[2]; // 2D representations sometimes... (x,y) order // 3x3 matrix - column major. X vector is 0, 1, 2, etc. // 0 3 6 // 1 4 7 // 2 5 8 typedef float M3DMatrix33f[9]; // A 3 x 3 matrix, column major (floats) - OpenGL Style typedef double M3DMatrix33d[9]; // A 3 x 3 matrix, column major (doubles) - OpenGL Style // 4x4 matrix - column major. X vector is 0, 1, 2, etc. // 0 4 8 12 // 1 5 9 13 // 2 6 10 14 // 3 7 11 15 typedef float M3DMatrix44f[16]; // A 4 X 4 matrix, column major (floats) - OpenGL style typedef double M3DMatrix44d[16]; // A 4 x 4 matrix, column major (doubles) - OpenGL style /////////////////////////////////////////////////////////////////////////////// // Useful constants #define M3D_PI (3.14159265358979323846) #define M3D_2PI (2.0 * M3D_PI) #define M3D_PI_DIV_180 (0.017453292519943296) #define M3D_INV_PI_DIV_180 (57.2957795130823229) /////////////////////////////////////////////////////////////////////////////// // Useful shortcuts and macros // Radians are king... but we need a way to swap back and forth #define m3dDegToRad(x) ((x)*M3D_PI_DIV_180) #define m3dRadToDeg(x) ((x)*M3D_INV_PI_DIV_180) // Hour angles #define m3dHrToDeg(x) ((x) * (1.0 / 15.0)) #define m3dHrToRad(x) m3dDegToRad(m3dHrToDeg(x)) #define m3dDegToHr(x) ((x) * 15.0)) #define m3dRadToHr(x) m3dDegToHr(m3dRadToDeg(x)) // Returns the same number if it is a power of // two. Returns a larger integer if it is not a // power of two. The larger integer is the next // highest power of two. inline unsigned int m3dIsPOW2(unsigned int iValue) { unsigned int nPow2 = 1; while(iValue > nPow2) nPow2 = (nPow2 << 1); return nPow2; } /////////////////////////////////////////////////////////////////////////////// // Inline accessor functions for people who just can't count to 3 - Vectors #define m3dGetVectorX(v) (v[0]) #define m3dGetVectorY(v) (v[1]) #define m3dGetVectorZ(v) (v[2]) #define m3dGetVectorW(v) (v[3]) #define m3dSetVectorX(v, x) ((v)[0] = (x)) #define m3dSetVectorY(v, y) ((v)[1] = (y)) #define m3dSetVectorZ(v, z) ((v)[2] = (z)) #define m3dSetVectorW(v, w) ((v)[3] = (w)) /////////////////////////////////////////////////////////////////////////////// // Inline vector functions // Load Vector with (x, y, z, w). inline void m3dLoadVector2(M3DVector2f v, float x, float y) { v[0] = x; v[1] = y; } inline void m3dLoadVector2(M3DVector2d v, float x, float y) { v[0] = x; v[1] = y; } inline void m3dLoadVector3(M3DVector3f v, float x, float y, float z) { v[0] = x; v[1] = y; v[2] = z; } inline void m3dLoadVector3(M3DVector3d v, double x, double y, double z) { v[0] = x; v[1] = y; v[2] = z; } inline void m3dLoadVector4(M3DVector4f v, float x, float y, float z, float w) { v[0] = x; v[1] = y; v[2] = z; v[3] = w;} inline void m3dLoadVector4(M3DVector4d v, double x, double y, double z, double w) { v[0] = x; v[1] = y; v[2] = z; v[3] = w;} //////////////////////////////////////////////////////////////////////////////// // Copy vector src into vector dst inline void m3dCopyVector2(M3DVector2f dst, const M3DVector2f src) { memcpy(dst, src, sizeof(M3DVector2f)); } inline void m3dCopyVector2(M3DVector2d dst, const M3DVector2d src) { memcpy(dst, src, sizeof(M3DVector2d)); } inline void m3dCopyVector3(M3DVector3f dst, const M3DVector3f src) { memcpy(dst, src, sizeof(M3DVector3f)); } inline void m3dCopyVector3(M3DVector3d dst, const M3DVector3d src) { memcpy(dst, src, sizeof(M3DVector3d)); } inline void m3dCopyVector4(M3DVector4f dst, const M3DVector4f src) { memcpy(dst, src, sizeof(M3DVector4f)); } inline void m3dCopyVector4(M3DVector4d dst, const M3DVector4d src) { memcpy(dst, src, sizeof(M3DVector4d)); } //////////////////////////////////////////////////////////////////////////////// // Add Vectors (r, a, b) r = a + b inline void m3dAddVectors2(M3DVector2f r, const M3DVector2f a, const M3DVector2f b) { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; } inline void m3dAddVectors2(M3DVector2d r, const M3DVector2d a, const M3DVector2d b) { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; } inline void m3dAddVectors3(M3DVector3f r, const M3DVector3f a, const M3DVector3f b) { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; r[2] = a[2] + b[2]; } inline void m3dAddVectors3(M3DVector3d r, const M3DVector3d a, const M3DVector3d b) { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; r[2] = a[2] + b[2]; } inline void m3dAddVectors4(M3DVector4f r, const M3DVector4f a, const M3DVector4f b) { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; r[2] = a[2] + b[2]; r[3] = a[3] + b[3]; } inline void m3dAddVectors4(M3DVector4d r, const M3DVector4d a, const M3DVector4d b) { r[0] = a[0] + b[0]; r[1] = a[1] + b[1]; r[2] = a[2] + b[2]; r[3] = a[3] + b[3]; } //////////////////////////////////////////////////////////////////////////////// // Subtract Vectors (r, a, b) r = a - b inline void m3dSubtractVectors2(M3DVector2f r, const M3DVector2f a, const M3DVector2f b) { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; } inline void m3dSubtractVectors2(M3DVector2d r, const M3DVector2d a, const M3DVector2d b) { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; } inline void m3dSubtractVectors3(M3DVector3f r, const M3DVector3f a, const M3DVector3f b) { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; r[2] = a[2] - b[2]; } inline void m3dSubtractVectors3(M3DVector3d r, const M3DVector3d a, const M3DVector3d b) { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; r[2] = a[2] - b[2]; } inline void m3dSubtractVectors4(M3DVector4f r, const M3DVector4f a, const M3DVector4f b) { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; r[2] = a[2] - b[2]; r[3] = a[3] - b[3]; } inline void m3dSubtractVectors4(M3DVector4d r, const M3DVector4d a, const M3DVector4d b) { r[0] = a[0] - b[0]; r[1] = a[1] - b[1]; r[2] = a[2] - b[2]; r[3] = a[3] - b[3]; } /////////////////////////////////////////////////////////////////////////////////////// // Scale Vectors (in place) inline void m3dScaleVector2(M3DVector2f v, float scale) { v[0] *= scale; v[1] *= scale; } inline void m3dScaleVector2(M3DVector2d v, double scale) { v[0] *= scale; v[1] *= scale; } inline void m3dScaleVector3(M3DVector3f v, float scale) { v[0] *= scale; v[1] *= scale; v[2] *= scale; } inline void m3dScaleVector3(M3DVector3d v, double scale) { v[0] *= scale; v[1] *= scale; v[2] *= scale; } inline void m3dScaleVector4(M3DVector4f v, float scale) { v[0] *= scale; v[1] *= scale; v[2] *= scale; v[3] *= scale; } inline void m3dScaleVector4(M3DVector4d v, double scale) { v[0] *= scale; v[1] *= scale; v[2] *= scale; v[3] *= scale; } ////////////////////////////////////////////////////////////////////////////////////// // Cross Product // u x v = result // We only need one version for floats, and one version for doubles. A 3 component // vector fits in a 4 component vector. If M3DVector4d or M3DVector4f are passed // we will be OK because 4th component is not used. inline void m3dCrossProduct(M3DVector3f result, const M3DVector3f u, const M3DVector3f v) { result[0] = u[1]*v[2] - v[1]*u[2]; result[1] = -u[0]*v[2] + v[0]*u[2]; result[2] = u[0]*v[1] - v[0]*u[1]; } inline void m3dCrossProduct(M3DVector3d result, const M3DVector3d u, const M3DVector3d v) { result[0] = u[1]*v[2] - v[1]*u[2]; result[1] = -u[0]*v[2] + v[0]*u[2]; result[2] = u[0]*v[1] - v[0]*u[1]; } ////////////////////////////////////////////////////////////////////////////////////// // Dot Product, only for three component vectors // return u dot v inline float m3dDotProduct(const M3DVector3f u, const M3DVector3f v) { return u[0]*v[0] + u[1]*v[1] + u[2]*v[2]; } inline double m3dDotProduct(const M3DVector3d u, const M3DVector3d v) { return u[0]*v[0] + u[1]*v[1] + u[2]*v[2]; } ////////////////////////////////////////////////////////////////////////////////////// // Angle between vectors, only for three component vectors. Angle is in radians... inline float m3dGetAngleBetweenVectors(const M3DVector3f u, const M3DVector3f v) { float dTemp = m3dDotProduct(u, v); return float(acos(double(dTemp))); } inline double m3dGetAngleBetweenVectors(const M3DVector3d u, const M3DVector3d v) { double dTemp = m3dDotProduct(u, v); return acos(dTemp); } ////////////////////////////////////////////////////////////////////////////////////// // Get Square of a vectors length // Only for three component vectors inline float m3dGetVectorLengthSquared(const M3DVector3f u) { return (u[0] * u[0]) + (u[1] * u[1]) + (u[2] * u[2]); } inline double m3dGetVectorLengthSquared(const M3DVector3d u) { return (u[0] * u[0]) + (u[1] * u[1]) + (u[2] * u[2]); } ////////////////////////////////////////////////////////////////////////////////////// // Get lenght of vector // Only for three component vectors. inline float m3dGetVectorLength(const M3DVector3f u) { return float(sqrt(double(m3dGetVectorLengthSquared(u)))); } inline double m3dGetVectorLength(const M3DVector3d u) { return sqrt(m3dGetVectorLengthSquared(u)); } ////////////////////////////////////////////////////////////////////////////////////// // Normalize a vector // Scale a vector to unit length. Easy, just scale the vector by it's length inline void m3dNormalizeVector(M3DVector3f u) { m3dScaleVector3(u, 1.0f / m3dGetVectorLength(u)); } inline void m3dNormalizeVector(M3DVector3d u) { m3dScaleVector3(u, 1.0 / m3dGetVectorLength(u)); } ////////////////////////////////////////////////////////////////////////////////////// // Get the distance between two points. The distance between two points is just // the magnitude of the difference between two vectors // Located in math.cpp float m3dGetDistanceSquared(const M3DVector3f u, const M3DVector3f v); double m3dGetDistanceSquared(const M3DVector3d u, const M3DVector3d v); inline double m3dGetDistance(const M3DVector3d u, const M3DVector3d v) { return sqrt(m3dGetDistanceSquared(u, v)); } inline float m3dGetDistance(const M3DVector3f u, const M3DVector3f v) { return float(sqrt(m3dGetDistanceSquared(u, v))); } inline float m3dGetMagnitudeSquared(const M3DVector3f u) { return u[0]*u[0] + u[1]*u[1] + u[2]*u[2]; } inline double m3dGetMagnitudeSquared(const M3DVector3d u) { return u[0]*u[0] + u[1]*u[1] + u[2]*u[2]; } inline float m3dGetMagnitude(const M3DVector3f u) { return float(sqrt(m3dGetMagnitudeSquared(u))); } inline double m3dGetMagnitude(const M3DVector3d u) { return sqrt(m3dGetMagnitudeSquared(u)); } ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// // Matrix functions // Both floating point and double precision 3x3 and 4x4 matricies are supported. // No support is included for arbitrarily dimensioned matricies on purpose, since // the 3x3 and 4x4 matrix routines are the most common for the purposes of this // library. Matrices are column major, like OpenGL matrices. // Unlike the vector functions, some of these are going to have to not be inlined, // although many will be. // Copy Matrix // Brain-dead memcpy inline void m3dCopyMatrix33(M3DMatrix33f dst, const M3DMatrix33f src) { memcpy(dst, src, sizeof(M3DMatrix33f)); } inline void m3dCopyMatrix33(M3DMatrix33d dst, const M3DMatrix33d src) { memcpy(dst, src, sizeof(M3DMatrix33d)); } inline void m3dCopyMatrix44(M3DMatrix44f dst, const M3DMatrix44f src) { memcpy(dst, src, sizeof(M3DMatrix44f)); } inline void m3dCopyMatrix44(M3DMatrix44d dst, const M3DMatrix44d src) { memcpy(dst, src, sizeof(M3DMatrix44d)); } // LoadIdentity // Implemented in Math3d.cpp void m3dLoadIdentity33(M3DMatrix33f m); void m3dLoadIdentity33(M3DMatrix33d m); void m3dLoadIdentity44(M3DMatrix44f m); void m3dLoadIdentity44(M3DMatrix44d m); ///////////////////////////////////////////////////////////////////////////// // Get/Set Column. inline void m3dGetMatrixColumn33(M3DVector3f dst, const M3DMatrix33f src, int column) { memcpy(dst, src + (3 * column), sizeof(float) * 3); } inline void m3dGetMatrixColumn33(M3DVector3d dst, const M3DMatrix33d src, int column) { memcpy(dst, src + (3 * column), sizeof(double) * 3); } inline void m3dSetMatrixColumn33(M3DMatrix33f dst, const M3DVector3f src, int column) { memcpy(dst + (3 * column), src, sizeof(float) * 3); } inline void m3dSetMatrixColumn33(M3DMatrix33d dst, const M3DVector3d src, int column) { memcpy(dst + (3 * column), src, sizeof(double) * 3); } inline void m3dGetMatrixColumn44(M3DVector4f dst, const M3DMatrix44f src, int column) { memcpy(dst, src + (4 * column), sizeof(float) * 4); } inline void m3dGetMatrixColumn44(M3DVector4d dst, const M3DMatrix44d src, int column) { memcpy(dst, src + (4 * column), sizeof(double) * 4); } inline void m3dSetMatrixColumn44(M3DMatrix44f dst, const M3DVector4f src, int column) { memcpy(dst + (4 * column), src, sizeof(float) * 4); } inline void m3dSetMatrixColumn44(M3DMatrix44d dst, const M3DVector4d src, int column) { memcpy(dst + (4 * column), src, sizeof(double) * 4); } // Get/Set row purposely omitted... use the functions below. // I don't think row vectors are useful for column major ordering... // If I'm wrong, add them later. ////////////////////////////////////////////////////////////////////////////// // Get/Set RowCol - Remember column major ordering... // Provides for element addressing inline void m3dSetMatrixRowCol33(M3DMatrix33f m, int row, int col, float value) { m[(col * 3) + row] = value; } inline float m3dGetMatrixRowCol33(const M3DMatrix33f m, int row, int col) { return m[(col * 3) + row]; } inline void m3dSetMatrixRowCol33(M3DMatrix33d m, int row, int col, double value) { m[(col * 3) + row] = value; } inline double m3dGetMatrixRowCol33(const M3DMatrix33d m, int row, int col) { return m[(col * 3) + row]; } inline void m3dSetMatrixRowCol44(M3DMatrix44f m, int row, int col, float value) { m[(col * 4) + row] = value; } inline float m3dGetMatrixRowCol44(const M3DMatrix44f m, int row, int col) { return m[(col * 4) + row]; } inline void m3dSetMatrixRowCol44(M3DMatrix44d m, int row, int col, double value) { m[(col * 4) + row] = value; } inline double m3dGetMatrixRowCol44(const M3DMatrix44d m, int row, int col) { return m[(col * 4) + row]; } /////////////////////////////////////////////////////////////////////////////// // Extract a rotation matrix from a 4x4 matrix // Extracts the rotation matrix (3x3) from a 4x4 matrix inline void m3dExtractRotation(M3DMatrix33f dst, const M3DMatrix44f src) { memcpy(dst, src, sizeof(float) * 3); // X column memcpy(dst + 3, src + 4, sizeof(float) * 3); // Y column memcpy(dst + 6, src + 8, sizeof(float) * 3); // Z column } // Ditto above, but for doubles inline void m3dExtractRotation(M3DMatrix33d dst, const M3DMatrix44d src) { memcpy(dst, src, sizeof(double) * 3); // X column memcpy(dst + 3, src + 4, sizeof(double) * 3); // Y column memcpy(dst + 6, src + 8, sizeof(double) * 3); // Z column } // Inject Rotation (3x3) into a full 4x4 matrix... inline void m3dInjectRotation(M3DMatrix44f dst, const M3DMatrix33f src) { memcpy(dst, src, sizeof(float) * 4); memcpy(dst + 4, src + 4, sizeof(float) * 4); memcpy(dst + 8, src + 8, sizeof(float) * 4); } // Ditto above for doubles inline void m3dInjectRotation(M3DMatrix44d dst, const M3DMatrix33d src) { memcpy(dst, src, sizeof(double) * 4); memcpy(dst + 4, src + 4, sizeof(double) * 4); memcpy(dst + 8, src + 8, sizeof(double) * 4); } //////////////////////////////////////////////////////////////////////////////// // MultMatrix // Implemented in Math.cpp void m3dMatrixMultiply44(M3DMatrix44f product, const M3DMatrix44f a, const M3DMatrix44f b); void m3dMatrixMultiply44(M3DMatrix44d product, const M3DMatrix44d a, const M3DMatrix44d b); void m3dMatrixMultiply33(M3DMatrix33f product, const M3DMatrix33f a, const M3DMatrix33f b); void m3dMatrixMultiply33(M3DMatrix33d product, const M3DMatrix33d a, const M3DMatrix33d b); // Transform - Does rotation and translation via a 4x4 matrix. Transforms // a point or vector. // By-the-way __inline means I'm asking the compiler to do a cost/benefit analysis. If // these are used frequently, they may not be inlined to save memory. I'm experimenting // with this.... __inline void m3dTransformVector3(M3DVector3f vOut, const M3DVector3f v, const M3DMatrix44f m) { vOut[0] = m[0] * v[0] + m[4] * v[1] + m[8] * v[2] + m[12];// * v[3]; vOut[1] = m[1] * v[0] + m[5] * v[1] + m[9] * v[2] + m[13];// * v[3]; vOut[2] = m[2] * v[0] + m[6] * v[1] + m[10] * v[2] + m[14];// * v[3]; //vOut[3] = m[3] * v[0] + m[7] * v[1] + m[11] * v[2] + m[15] * v[3]; } // Ditto above, but for doubles __inline void m3dTransformVector3(M3DVector3d vOut, const M3DVector3d v, const M3DMatrix44d m) { vOut[0] = m[0] * v[0] + m[4] * v[1] + m[8] * v[2] + m[12];// * v[3]; vOut[1] = m[1] * v[0] + m[5] * v[1] + m[9] * v[2] + m[13];// * v[3]; vOut[2] = m[2] * v[0] + m[6] * v[1] + m[10] * v[2] + m[14];// * v[3]; //vOut[3] = m[3] * v[0] + m[7] * v[1] + m[11] * v[2] + m[15] * v[3]; } __inline void m3dTransformVector4(M3DVector4f vOut, const M3DVector4f v, const M3DMatrix44f m) { vOut[0] = m[0] * v[0] + m[4] * v[1] + m[8] * v[2] + m[12] * v[3]; vOut[1] = m[1] * v[0] + m[5] * v[1] + m[9] * v[2] + m[13] * v[3]; vOut[2] = m[2] * v[0] + m[6] * v[1] + m[10] * v[2] + m[14] * v[3]; vOut[3] = m[3] * v[0] + m[7] * v[1] + m[11] * v[2] + m[15] * v[3]; } // Ditto above, but for doubles __inline void m3dTransformVector4(M3DVector4d vOut, const M3DVector4d v, const M3DMatrix44d m) { vOut[0] = m[0] * v[0] + m[4] * v[1] + m[8] * v[2] + m[12] * v[3]; vOut[1] = m[1] * v[0] + m[5] * v[1] + m[9] * v[2] + m[13] * v[3]; vOut[2] = m[2] * v[0] + m[6] * v[1] + m[10] * v[2] + m[14] * v[3]; vOut[3] = m[3] * v[0] + m[7] * v[1] + m[11] * v[2] + m[15] * v[3]; } // Just do the rotation, not the translation... this is usually done with a 3x3 // Matrix. __inline void m3dRotateVector(M3DVector3f vOut, const M3DVector3f p, const M3DMatrix33f m) { vOut[0] = m[0] * p[0] + m[3] * p[1] + m[6] * p[2]; vOut[1] = m[1] * p[0] + m[4] * p[1] + m[7] * p[2]; vOut[2] = m[2] * p[0] + m[5] * p[1] + m[8] * p[2]; } // Ditto above, but for doubles __inline void m3dRotateVector(M3DVector3d vOut, const M3DVector3d p, const M3DMatrix33d m) { vOut[0] = m[0] * p[0] + m[3] * p[1] + m[6] * p[2]; vOut[1] = m[1] * p[0] + m[4] * p[1] + m[7] * p[2]; vOut[2] = m[2] * p[0] + m[5] * p[1] + m[8] * p[2]; } // Scale a matrix (I don't beleive in Scaling matricies ;-) // Yes, it's faster to loop backwards... These could be // unrolled... but eh... if you find this is a bottleneck, // then you should unroll it yourself inline void m3dScaleMatrix33(M3DMatrix33f m, float scale) { for(int i = 8; i >=0; i--) m[i] *= scale; } inline void m3dScaleMatrix33(M3DMatrix33d m, double scale) { for(int i = 8; i >=0; i--) m[i] *= scale; } inline void m3dScaleMatrix44(M3DMatrix44f m, float scale) { for(int i = 15; i >=0; i--) m[i] *= scale; } inline void m3dScaleMatrix44(M3DMatrix44d m, double scale) { for(int i = 15; i >=0; i--) m[i] *= scale; } // Create a Rotation matrix // Implemented in math.cpp void m3dRotationMatrix33(M3DMatrix33f m, float angle, float x, float y, float z); void m3dRotationMatrix33(M3DMatrix33d m, double angle, double x, double y, double z); void m3dRotationMatrix44(M3DMatrix44f m, float angle, float x, float y, float z); void m3dRotationMatrix44(M3DMatrix44d m, double angle, double x, double y, double z); // Create a Translation matrix. Only 4x4 matrices have translation components inline void m3dTranslationMatrix44(M3DMatrix44f m, float x, float y, float z) { m3dLoadIdentity44(m); m[12] = x; m[13] = y; m[14] = z; } inline void m3dTranslationMatrix44(M3DMatrix44d m, double x, double y, double z) { m3dLoadIdentity44(m); m[12] = x; m[13] = y; m[14] = z; } // Translate matrix. Only 4x4 matrices supported inline void m3dTranslateMatrix44(M3DMatrix44f m, float x, float y, float z) { m[12] += x; m[13] += y; m[14] += z; } inline void m3dTranslateMatrix44(M3DMatrix44d m, double x, double y, double z) { m[12] += x; m[13] += y; m[14] += z; } // Scale matrix. Only 4x4 matrices supported inline void m3dScaleMatrix44(M3DMatrix44f m, float x, float y, float z) { m[0] *= x; m[5] *= y; m[10] *= z; } inline void m3dScaleMatrix44(M3DMatrix44d m, double x, double y, double z) { m[0] *= x; m[5] *= y; m[10] *= z; } // Transpose/Invert - Only 4x4 matricies supported #define TRANSPOSE44(dst, src) \ { \ for (int j = 0; j < 4; j++) \ { \ for (int i = 0; i < 4; i++) \ { \ dst[(j*4)+i] = src[(i*4)+j]; \ } \ } \ } inline void m3dTransposeMatrix44(M3DMatrix44f dst, const M3DMatrix44f src) { TRANSPOSE44(dst, src); } inline void m3dTransposeMatrix44(M3DMatrix44d dst, const M3DMatrix44d src) { TRANSPOSE44(dst, src); } bool m3dInvertMatrix44(M3DMatrix44f dst, const M3DMatrix44f src); bool m3dInvertMatrix44(M3DMatrix44d dst, const M3DMatrix44d src); /////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////// // Other Miscellaneous functions // Find a normal from three points // Implemented in math3d.cpp void m3dFindNormal(M3DVector3f result, const M3DVector3f point1, const M3DVector3f point2, const M3DVector3f point3); void m3dFindNormal(M3DVector3d result, const M3DVector3d point1, const M3DVector3d point2, const M3DVector3d point3); // Calculates the signed distance of a point to a plane inline float m3dGetDistanceToPlane(const M3DVector3f point, const M3DVector4f plane) { return point[0]*plane[0] + point[1]*plane[1] + point[2]*plane[2] + plane[3]; } inline double m3dGetDistanceToPlane(const M3DVector3d point, const M3DVector4d plane) { return point[0]*plane[0] + point[1]*plane[1] + point[2]*plane[2] + plane[3]; } // Get plane equation from three points and a normal void m3dGetPlaneEquation(M3DVector4f planeEq, const M3DVector3f p1, const M3DVector3f p2, const M3DVector3f p3); void m3dGetPlaneEquation(M3DVector4d planeEq, const M3DVector3d p1, const M3DVector3d p2, const M3DVector3d p3); // Determine if a ray intersects a sphere double m3dRaySphereTest(const M3DVector3d point, const M3DVector3d ray, const M3DVector3d sphereCenter, double sphereRadius); float m3dRaySphereTest(const M3DVector3f point, const M3DVector3f ray, const M3DVector3f sphereCenter, float sphereRadius); // Etc. etc. /////////////////////////////////////////////////////////////////////////////////////////////////////// // Faster (and more robust) replacements for gluProject void m3dProjectXY( M3DVector2f vPointOut, const M3DMatrix44f mModelView, const M3DMatrix44f mProjection, const int iViewPort[4], const M3DVector3f vPointIn); void m3dProjectXYZ(M3DVector3f vPointOut, const M3DMatrix44f mModelView, const M3DMatrix44f mProjection, const int iViewPort[4], const M3DVector3f vPointIn); ////////////////////////////////////////////////////////////////////////////////////////////////// // This function does a three dimensional Catmull-Rom "spline" interpolation between p1 and p2 void m3dCatmullRom(M3DVector3f vOut, M3DVector3f vP0, M3DVector3f vP1, M3DVector3f vP2, M3DVector3f vP3, float t); void m3dCatmullRom(M3DVector3d vOut, M3DVector3d vP0, M3DVector3d vP1, M3DVector3d vP2, M3DVector3d vP3, double t); ////////////////////////////////////////////////////////////////////////////////////////////////// // Compare floats and doubles... inline bool m3dCloseEnough(float fCandidate, float fCompare, float fEpsilon) { return (fabs(fCandidate - fCompare) < fEpsilon); } inline bool m3dCloseEnough(double dCandidate, double dCompare, double dEpsilon) { return (fabs(dCandidate - dCompare) < dEpsilon); } //////////////////////////////////////////////////////////////////////////// // Used for normal mapping. Finds the tangent bases for a triangle... // Only a floating point implementation is provided. void m3dCalculateTangentBasis(const M3DVector3f pvTriangle[3], const M3DVector2f pvTexCoords[3], const M3DVector3f N, M3DVector3f vTangent); //////////////////////////////////////////////////////////////////////////// // Smoothly step between 0 and 1 between edge1 and edge 2 double m3dSmoothStep(double edge1, double edge2, double x); float m3dSmoothStep(float edge1, float edge2, float x); ///////////////////////////////////////////////////////////////////////////// // Planar shadow Matrix void m3dMakePlanarShadowMatrix(M3DMatrix44d proj, const M3DVector4d planeEq, const M3DVector3d vLightPos); void m3dMakePlanarShadowMatrix(M3DMatrix44f proj, const M3DVector4f planeEq, const M3DVector3f vLightPos); double m3dClosestPointOnRay(M3DVector3d vPointOnRay, const M3DVector3d vRayOrigin, const M3DVector3d vUnitRayDir, const M3DVector3d vPointInSpace); float m3dClosestPointOnRay(M3DVector3f vPointOnRay, const M3DVector3f vRayOrigin, const M3DVector3f vUnitRayDir, const M3DVector3f vPointInSpace); #endif