// Math3d.c // Implementation of non-inlined functions in the Math3D Library // Richard S. Wright Jr. #include "math3d.h" //////////////////////////////////////////////////////////// // LoadIdentity // For 3x3 and 4x4 float and double matricies. // 3x3 float void m3dLoadIdentity33(M3DMatrix33f m) { // Don't be fooled, this is still column major static M3DMatrix33f identity = { 1.0f, 0.0f, 0.0f , 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 1.0f }; memcpy(m, identity, sizeof(M3DMatrix33f)); } // 3x3 double void m3dLoadIdentity33(M3DMatrix33d m) { // Don't be fooled, this is still column major static M3DMatrix33d identity = { 1.0, 0.0, 0.0 , 0.0, 1.0, 0.0, 0.0, 0.0, 1.0 }; memcpy(m, identity, sizeof(M3DMatrix33d)); } // 4x4 float void m3dLoadIdentity44(M3DMatrix44f m) { // Don't be fooled, this is still column major static M3DMatrix44f identity = { 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f }; memcpy(m, identity, sizeof(M3DMatrix44f)); } // 4x4 double void m3dLoadIdentity44(M3DMatrix44d m) { static M3DMatrix44d identity = { 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0 }; memcpy(m, identity, sizeof(M3DMatrix44d)); } //////////////////////////////////////////////////////////////////////// // Return the square of the distance between two points // Should these be inlined...? float m3dGetDistanceSquared(const M3DVector3f u, const M3DVector3f v) { float x = u[0] - v[0]; x = x*x; float y = u[1] - v[1]; y = y*y; float z = u[2] - v[2]; z = z*z; return (x + y + z); } // Ditto above, but for doubles double m3dGetDistanceSquared(const M3DVector3d u, const M3DVector3d v) { double x = u[0] - v[0]; x = x*x; double y = u[1] - v[1]; y = y*y; double z = u[2] - v[2]; z = z*z; return (x + y + z); } #define A(row,col) a[(col<<2)+row] #define B(row,col) b[(col<<2)+row] #define P(row,col) product[(col<<2)+row] /////////////////////////////////////////////////////////////////////////////// // Multiply two 4x4 matricies void m3dMatrixMultiply44(M3DMatrix44f product, const M3DMatrix44f a, const M3DMatrix44f b) { for (int i = 0; i < 4; i++) { float ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0); P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1); P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2); P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3); } } // Ditto above, but for doubles void m3dMatrixMultiply(M3DMatrix44d product, const M3DMatrix44d a, const M3DMatrix44d b) { for (int i = 0; i < 4; i++) { double ai0=A(i,0), ai1=A(i,1), ai2=A(i,2), ai3=A(i,3); P(i,0) = ai0 * B(0,0) + ai1 * B(1,0) + ai2 * B(2,0) + ai3 * B(3,0); P(i,1) = ai0 * B(0,1) + ai1 * B(1,1) + ai2 * B(2,1) + ai3 * B(3,1); P(i,2) = ai0 * B(0,2) + ai1 * B(1,2) + ai2 * B(2,2) + ai3 * B(3,2); P(i,3) = ai0 * B(0,3) + ai1 * B(1,3) + ai2 * B(2,3) + ai3 * B(3,3); } } #undef A #undef B #undef P #define A33(row,col) a[(col*3)+row] #define B33(row,col) b[(col*3)+row] #define P33(row,col) product[(col*3)+row] /////////////////////////////////////////////////////////////////////////////// // Multiply two 3x3 matricies void m3dMatrixMultiply33(M3DMatrix33f product, const M3DMatrix33f a, const M3DMatrix33f b) { for (int i = 0; i < 3; i++) { float ai0=A33(i,0), ai1=A33(i,1), ai2=A33(i,2); P33(i,0) = ai0 * B33(0,0) + ai1 * B33(1,0) + ai2 * B33(2,0); P33(i,1) = ai0 * B33(0,1) + ai1 * B33(1,1) + ai2 * B33(2,1); P33(i,2) = ai0 * B33(0,2) + ai1 * B33(1,2) + ai2 * B33(2,2); } } // Ditto above, but for doubles void m3dMatrixMultiply44(M3DMatrix33d product, const M3DMatrix33d a, const M3DMatrix33d b) { for (int i = 0; i < 3; i++) { double ai0=A33(i,0), ai1=A33(i,1), ai2=A33(i,2); P33(i,0) = ai0 * B33(0,0) + ai1 * B33(1,0) + ai2 * B33(2,0); P33(i,1) = ai0 * B33(0,1) + ai1 * B33(1,1) + ai2 * B33(2,1); P33(i,2) = ai0 * B33(0,2) + ai1 * B33(1,2) + ai2 * B33(2,2); } } #undef A33 #undef B33 #undef P33 #define M33(row,col) m[col*3+row] /////////////////////////////////////////////////////////////////////////////// // Creates a 3x3 rotation matrix, takes radians NOT degrees void m3dRotationMatrix33(M3DMatrix33f m, float angle, float x, float y, float z) { float mag, s, c; float xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c; s = float(sin(angle)); c = float(cos(angle)); mag = float(sqrt( x*x + y*y + z*z )); // Identity matrix if (mag == 0.0f) { m3dLoadIdentity33(m); return; } // Rotation matrix is normalized x /= mag; y /= mag; z /= mag; xx = x * x; yy = y * y; zz = z * z; xy = x * y; yz = y * z; zx = z * x; xs = x * s; ys = y * s; zs = z * s; one_c = 1.0f - c; M33(0,0) = (one_c * xx) + c; M33(0,1) = (one_c * xy) - zs; M33(0,2) = (one_c * zx) + ys; M33(1,0) = (one_c * xy) + zs; M33(1,1) = (one_c * yy) + c; M33(1,2) = (one_c * yz) - xs; M33(2,0) = (one_c * zx) - ys; M33(2,1) = (one_c * yz) + xs; M33(2,2) = (one_c * zz) + c; } #undef M33 /////////////////////////////////////////////////////////////////////////////// // Creates a 4x4 rotation matrix, takes radians NOT degrees void m3dRotationMatrix44(M3DMatrix44f m, float angle, float x, float y, float z) { float mag, s, c; float xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c; s = float(sin(angle)); c = float(cos(angle)); mag = float(sqrt( x*x + y*y + z*z )); // Identity matrix if (mag == 0.0f) { m3dLoadIdentity44(m); return; } // Rotation matrix is normalized x /= mag; y /= mag; z /= mag; #define M(row,col) m[col*4+row] xx = x * x; yy = y * y; zz = z * z; xy = x * y; yz = y * z; zx = z * x; xs = x * s; ys = y * s; zs = z * s; one_c = 1.0f - c; M(0,0) = (one_c * xx) + c; M(0,1) = (one_c * xy) - zs; M(0,2) = (one_c * zx) + ys; M(0,3) = 0.0f; M(1,0) = (one_c * xy) + zs; M(1,1) = (one_c * yy) + c; M(1,2) = (one_c * yz) - xs; M(1,3) = 0.0f; M(2,0) = (one_c * zx) - ys; M(2,1) = (one_c * yz) + xs; M(2,2) = (one_c * zz) + c; M(2,3) = 0.0f; M(3,0) = 0.0f; M(3,1) = 0.0f; M(3,2) = 0.0f; M(3,3) = 1.0f; #undef M } /////////////////////////////////////////////////////////////////////////////// // Ditto above, but for doubles void m3dRotationMatrix33(M3DMatrix33d m, double angle, double x, double y, double z) { double mag, s, c; double xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c; s = sin(angle); c = cos(angle); mag = sqrt( x*x + y*y + z*z ); // Identity matrix if (mag == 0.0) { m3dLoadIdentity33(m); return; } // Rotation matrix is normalized x /= mag; y /= mag; z /= mag; #define M(row,col) m[col*3+row] xx = x * x; yy = y * y; zz = z * z; xy = x * y; yz = y * z; zx = z * x; xs = x * s; ys = y * s; zs = z * s; one_c = 1.0 - c; M(0,0) = (one_c * xx) + c; M(0,1) = (one_c * xy) - zs; M(0,2) = (one_c * zx) + ys; M(1,0) = (one_c * xy) + zs; M(1,1) = (one_c * yy) + c; M(1,2) = (one_c * yz) - xs; M(2,0) = (one_c * zx) - ys; M(2,1) = (one_c * yz) + xs; M(2,2) = (one_c * zz) + c; #undef M } /////////////////////////////////////////////////////////////////////////////// // Creates a 4x4 rotation matrix, takes radians NOT degrees void m3dRotationMatrix44(M3DMatrix44d m, double angle, double x, double y, double z) { double mag, s, c; double xx, yy, zz, xy, yz, zx, xs, ys, zs, one_c; s = sin(angle); c = cos(angle); mag = sqrt( x*x + y*y + z*z ); // Identity matrix if (mag == 0.0) { m3dLoadIdentity44(m); return; } // Rotation matrix is normalized x /= mag; y /= mag; z /= mag; #define M(row,col) m[col*4+row] xx = x * x; yy = y * y; zz = z * z; xy = x * y; yz = y * z; zx = z * x; xs = x * s; ys = y * s; zs = z * s; one_c = 1.0f - c; M(0,0) = (one_c * xx) + c; M(0,1) = (one_c * xy) - zs; M(0,2) = (one_c * zx) + ys; M(0,3) = 0.0; M(1,0) = (one_c * xy) + zs; M(1,1) = (one_c * yy) + c; M(1,2) = (one_c * yz) - xs; M(1,3) = 0.0; M(2,0) = (one_c * zx) - ys; M(2,1) = (one_c * yz) + xs; M(2,2) = (one_c * zz) + c; M(2,3) = 0.0; M(3,0) = 0.0; M(3,1) = 0.0; M(3,2) = 0.0; M(3,3) = 1.0; #undef M } // Lifted from Mesa /* * Compute inverse of 4x4 transformation matrix. * Code contributed by Jacques Leroy jle@star.be * Return GL_TRUE for success, GL_FALSE for failure (singular matrix) */ bool m3dInvertMatrix44(M3DMatrix44f dst, const M3DMatrix44f src ) { #define SWAP_ROWS(a, b) { float *_tmp = a; (a)=(b); (b)=_tmp; } #define MAT(m,r,c) (m)[(c)*4+(r)] float wtmp[4][8]; float m0, m1, m2, m3, s; float *r0, *r1, *r2, *r3; r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3]; r0[0] = MAT(src,0,0), r0[1] = MAT(src,0,1), r0[2] = MAT(src,0,2), r0[3] = MAT(src,0,3), r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0, r1[0] = MAT(src,1,0), r1[1] = MAT(src,1,1), r1[2] = MAT(src,1,2), r1[3] = MAT(src,1,3), r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0, r2[0] = MAT(src,2,0), r2[1] = MAT(src,2,1), r2[2] = MAT(src,2,2), r2[3] = MAT(src,2,3), r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0, r3[0] = MAT(src,3,0), r3[1] = MAT(src,3,1), r3[2] = MAT(src,3,2), r3[3] = MAT(src,3,3), r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0; /* choose pivot - or die */ if (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2); if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1); if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0); if (0.0 == r0[0]) return false; /* eliminate first variable */ m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0]; s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s; s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s; s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s; s = r0[4]; if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; } s = r0[5]; if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; } s = r0[6]; if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; } s = r0[7]; if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; } /* choose pivot - or die */ if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2); if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1); if (0.0 == r1[1]) return false; /* eliminate second variable */ m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1]; r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2]; r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3]; s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; } s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; } s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; } s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; } /* choose pivot - or die */ if (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2); if (0.0 == r2[2]) return false; /* eliminate third variable */ m3 = r3[2]/r2[2]; r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4], r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7]; /* last check */ if (0.0 == r3[3]) return false; s = 1.0f/r3[3]; /* now back substitute row 3 */ r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s; m2 = r2[3]; /* now back substitute row 2 */ s = 1.0f/r2[2]; r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2), r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2); m1 = r1[3]; r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1, r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1; m0 = r0[3]; r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0, r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0; m1 = r1[2]; /* now back substitute row 1 */ s = 1.0f/r1[1]; r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1), r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1); m0 = r0[2]; r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0, r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0; m0 = r0[1]; /* now back substitute row 0 */ s = 1.0f/r0[0]; r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0), r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0); MAT(dst,0,0) = r0[4]; MAT(dst,0,1) = r0[5], MAT(dst,0,2) = r0[6]; MAT(dst,0,3) = r0[7], MAT(dst,1,0) = r1[4]; MAT(dst,1,1) = r1[5], MAT(dst,1,2) = r1[6]; MAT(dst,1,3) = r1[7], MAT(dst,2,0) = r2[4]; MAT(dst,2,1) = r2[5], MAT(dst,2,2) = r2[6]; MAT(dst,2,3) = r2[7], MAT(dst,3,0) = r3[4]; MAT(dst,3,1) = r3[5], MAT(dst,3,2) = r3[6]; MAT(dst,3,3) = r3[7]; return true; #undef MAT #undef SWAP_ROWS } // Ditto above, but for doubles bool m3dInvertMatrix44(M3DMatrix44d dst, const M3DMatrix44d src) { #define SWAP_ROWS(a, b) { double *_tmp = a; (a)=(b); (b)=_tmp; } #define MAT(m,r,c) (m)[(c)*4+(r)] double wtmp[4][8]; double m0, m1, m2, m3, s; double *r0, *r1, *r2, *r3; r0 = wtmp[0], r1 = wtmp[1], r2 = wtmp[2], r3 = wtmp[3]; r0[0] = MAT(src,0,0), r0[1] = MAT(src,0,1), r0[2] = MAT(src,0,2), r0[3] = MAT(src,0,3), r0[4] = 1.0, r0[5] = r0[6] = r0[7] = 0.0, r1[0] = MAT(src,1,0), r1[1] = MAT(src,1,1), r1[2] = MAT(src,1,2), r1[3] = MAT(src,1,3), r1[5] = 1.0, r1[4] = r1[6] = r1[7] = 0.0, r2[0] = MAT(src,2,0), r2[1] = MAT(src,2,1), r2[2] = MAT(src,2,2), r2[3] = MAT(src,2,3), r2[6] = 1.0, r2[4] = r2[5] = r2[7] = 0.0, r3[0] = MAT(src,3,0), r3[1] = MAT(src,3,1), r3[2] = MAT(src,3,2), r3[3] = MAT(src,3,3), r3[7] = 1.0, r3[4] = r3[5] = r3[6] = 0.0; // choose pivot - or die if (fabs(r3[0])>fabs(r2[0])) SWAP_ROWS(r3, r2); if (fabs(r2[0])>fabs(r1[0])) SWAP_ROWS(r2, r1); if (fabs(r1[0])>fabs(r0[0])) SWAP_ROWS(r1, r0); if (0.0 == r0[0]) return false; // eliminate first variable m1 = r1[0]/r0[0]; m2 = r2[0]/r0[0]; m3 = r3[0]/r0[0]; s = r0[1]; r1[1] -= m1 * s; r2[1] -= m2 * s; r3[1] -= m3 * s; s = r0[2]; r1[2] -= m1 * s; r2[2] -= m2 * s; r3[2] -= m3 * s; s = r0[3]; r1[3] -= m1 * s; r2[3] -= m2 * s; r3[3] -= m3 * s; s = r0[4]; if (s != 0.0) { r1[4] -= m1 * s; r2[4] -= m2 * s; r3[4] -= m3 * s; } s = r0[5]; if (s != 0.0) { r1[5] -= m1 * s; r2[5] -= m2 * s; r3[5] -= m3 * s; } s = r0[6]; if (s != 0.0) { r1[6] -= m1 * s; r2[6] -= m2 * s; r3[6] -= m3 * s; } s = r0[7]; if (s != 0.0) { r1[7] -= m1 * s; r2[7] -= m2 * s; r3[7] -= m3 * s; } // choose pivot - or die if (fabs(r3[1])>fabs(r2[1])) SWAP_ROWS(r3, r2); if (fabs(r2[1])>fabs(r1[1])) SWAP_ROWS(r2, r1); if (0.0 == r1[1]) return false; // eliminate second variable m2 = r2[1]/r1[1]; m3 = r3[1]/r1[1]; r2[2] -= m2 * r1[2]; r3[2] -= m3 * r1[2]; r2[3] -= m2 * r1[3]; r3[3] -= m3 * r1[3]; s = r1[4]; if (0.0 != s) { r2[4] -= m2 * s; r3[4] -= m3 * s; } s = r1[5]; if (0.0 != s) { r2[5] -= m2 * s; r3[5] -= m3 * s; } s = r1[6]; if (0.0 != s) { r2[6] -= m2 * s; r3[6] -= m3 * s; } s = r1[7]; if (0.0 != s) { r2[7] -= m2 * s; r3[7] -= m3 * s; } // choose pivot - or die if (fabs(r3[2])>fabs(r2[2])) SWAP_ROWS(r3, r2); if (0.0 == r2[2]) return false; // eliminate third variable m3 = r3[2]/r2[2]; r3[3] -= m3 * r2[3], r3[4] -= m3 * r2[4], r3[5] -= m3 * r2[5], r3[6] -= m3 * r2[6], r3[7] -= m3 * r2[7]; // last check if (0.0 == r3[3]) return false; s = 1.0f/r3[3]; // now back substitute row 3 r3[4] *= s; r3[5] *= s; r3[6] *= s; r3[7] *= s; m2 = r2[3]; // now back substitute row 2 s = 1.0f/r2[2]; r2[4] = s * (r2[4] - r3[4] * m2), r2[5] = s * (r2[5] - r3[5] * m2), r2[6] = s * (r2[6] - r3[6] * m2), r2[7] = s * (r2[7] - r3[7] * m2); m1 = r1[3]; r1[4] -= r3[4] * m1, r1[5] -= r3[5] * m1, r1[6] -= r3[6] * m1, r1[7] -= r3[7] * m1; m0 = r0[3]; r0[4] -= r3[4] * m0, r0[5] -= r3[5] * m0, r0[6] -= r3[6] * m0, r0[7] -= r3[7] * m0; m1 = r1[2]; // now back substitute row 1 s = 1.0f/r1[1]; r1[4] = s * (r1[4] - r2[4] * m1), r1[5] = s * (r1[5] - r2[5] * m1), r1[6] = s * (r1[6] - r2[6] * m1), r1[7] = s * (r1[7] - r2[7] * m1); m0 = r0[2]; r0[4] -= r2[4] * m0, r0[5] -= r2[5] * m0, r0[6] -= r2[6] * m0, r0[7] -= r2[7] * m0; m0 = r0[1]; // now back substitute row 0 s = 1.0f/r0[0]; r0[4] = s * (r0[4] - r1[4] * m0), r0[5] = s * (r0[5] - r1[5] * m0), r0[6] = s * (r0[6] - r1[6] * m0), r0[7] = s * (r0[7] - r1[7] * m0); MAT(dst,0,0) = r0[4]; MAT(dst,0,1) = r0[5], MAT(dst,0,2) = r0[6]; MAT(dst,0,3) = r0[7], MAT(dst,1,0) = r1[4]; MAT(dst,1,1) = r1[5], MAT(dst,1,2) = r1[6]; MAT(dst,1,3) = r1[7], MAT(dst,2,0) = r2[4]; MAT(dst,2,1) = r2[5], MAT(dst,2,2) = r2[6]; MAT(dst,2,3) = r2[7], MAT(dst,3,0) = r3[4]; MAT(dst,3,1) = r3[5], MAT(dst,3,2) = r3[6]; MAT(dst,3,3) = r3[7]; return true; #undef MAT #undef SWAP_ROWS return true; } /////////////////////////////////////////////////////////////////////////////////////// // Get Window coordinates, discard Z... void m3dProjectXY(const M3DMatrix44f mModelView, const M3DMatrix44f mProjection, const int iViewPort[4], const M3DVector3f vPointIn, M3DVector2f vPointOut) { M3DVector4f vBack, vForth; memcpy(vBack, vPointIn, sizeof(float)*3); vBack[3] = 1.0f; m3dTransformVector4(vForth, vBack, mModelView); m3dTransformVector4(vBack, vForth, mProjection); if (!m3dCloseEnough(vBack[3], 0.0f, 0.000001f)) { float div = 1.0f / vBack[3]; vBack[0] *= div; vBack[1] *= div; } vPointOut[0] = vBack[0] * 0.5f + 0.5f; vPointOut[1] = vBack[1] * 0.5f + 0.5f; /* Map x,y to viewport */ vPointOut[0] = (vPointOut[0] * iViewPort[2]) + iViewPort[0]; vPointOut[1] = (vPointOut[1] * iViewPort[3]) + iViewPort[1]; } /////////////////////////////////////////////////////////////////////////////////////// // Get window coordinates, we also want Z.... void m3dProjectXYZ(const M3DMatrix44f mModelView, const M3DMatrix44f mProjection, const int iViewPort[4], const M3DVector3f vPointIn, M3DVector3f vPointOut) { M3DVector4f vBack, vForth; memcpy(vBack, vPointIn, sizeof(float)*3); vBack[3] = 1.0f; m3dTransformVector4(vForth, vBack, mModelView); m3dTransformVector4(vBack, vForth, mProjection); if (!m3dCloseEnough(vBack[3], 0.0f, 0.000001f)) { float div = 1.0f / vBack[3]; vBack[0] *= div; vBack[1] *= div; vBack[2] *= div; } vPointOut[0] = vBack[0] * 0.5f + 0.5f; vPointOut[1] = vBack[1] * 0.5f + 0.5f; vPointOut[2] = vBack[2] * 0.5f + 0.5f; /* Map x,y to viewport */ vPointOut[0] = (vPointOut[0] * iViewPort[2]) + iViewPort[0]; vPointOut[1] = (vPointOut[1] * iViewPort[3]) + iViewPort[1]; } /////////////////////////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////////////////////////// // Misc. Utilities /////////////////////////////////////////////////////////////////////////////// // Calculates the normal of a triangle specified by the three points // p1, p2, and p3. Each pointer points to an array of three floats. The // triangle is assumed to be wound counter clockwise. void m3dFindNormal(M3DVector3f result, const M3DVector3f point1, const M3DVector3f point2, const M3DVector3f point3) { M3DVector3f v1,v2; // Temporary vectors // Calculate two vectors from the three points. Assumes counter clockwise // winding! v1[0] = point1[0] - point2[0]; v1[1] = point1[1] - point2[1]; v1[2] = point1[2] - point2[2]; v2[0] = point2[0] - point3[0]; v2[1] = point2[1] - point3[1]; v2[2] = point2[2] - point3[2]; // Take the cross product of the two vectors to get // the normal vector. m3dCrossProduct(result, v1, v2); } // Ditto above, but for doubles void m3dFindNormal(M3DVector3d result, const M3DVector3d point1, const M3DVector3d point2, const M3DVector3d point3) { M3DVector3d v1,v2; // Temporary vectors // Calculate two vectors from the three points. Assumes counter clockwise // winding! v1[0] = point1[0] - point2[0]; v1[1] = point1[1] - point2[1]; v1[2] = point1[2] - point2[2]; v2[0] = point2[0] - point3[0]; v2[1] = point2[1] - point3[1]; v2[2] = point2[2] - point3[2]; // Take the cross product of the two vectors to get // the normal vector. m3dCrossProduct(result, v1, v2); } ///////////////////////////////////////////////////////////////////////////////////////// // Calculate the plane equation of the plane that the three specified points lay in. The // points are given in clockwise winding order, with normal pointing out of clockwise face // planeEq contains the A,B,C, and D of the plane equation coefficients void m3dGetPlaneEquation(M3DVector4f planeEq, const M3DVector3f p1, const M3DVector3f p2, const M3DVector3f p3) { // Get two vectors... do the cross product M3DVector3f v1, v2; // V1 = p3 - p1 v1[0] = p3[0] - p1[0]; v1[1] = p3[1] - p1[1]; v1[2] = p3[2] - p1[2]; // V2 = P2 - p1 v2[0] = p2[0] - p1[0]; v2[1] = p2[1] - p1[1]; v2[2] = p2[2] - p1[2]; // Unit normal to plane - Not sure which is the best way here m3dCrossProduct(planeEq, v1, v2); m3dNormalizeVector(planeEq); // Back substitute to get D planeEq[3] = -(planeEq[0] * p3[0] + planeEq[1] * p3[1] + planeEq[2] * p3[2]); } // Ditto above, but for doubles void m3dGetPlaneEquation(M3DVector4d planeEq, const M3DVector3d p1, const M3DVector3d p2, const M3DVector3d p3) { // Get two vectors... do the cross product M3DVector3d v1, v2; // V1 = p3 - p1 v1[0] = p3[0] - p1[0]; v1[1] = p3[1] - p1[1]; v1[2] = p3[2] - p1[2]; // V2 = P2 - p1 v2[0] = p2[0] - p1[0]; v2[1] = p2[1] - p1[1]; v2[2] = p2[2] - p1[2]; // Unit normal to plane - Not sure which is the best way here m3dCrossProduct(planeEq, v1, v2); m3dNormalizeVector(planeEq); // Back substitute to get D planeEq[3] = -(planeEq[0] * p3[0] + planeEq[1] * p3[1] + planeEq[2] * p3[2]); } ////////////////////////////////////////////////////////////////////////////////////////////////// // This function does a three dimensional Catmull-Rom curve interpolation. Pass four points, and a // floating point number between 0.0 and 1.0. The curve is interpolated between the middle two points. // Coded by RSW // http://www.mvps.org/directx/articles/catmull/ void m3dCatmullRom3(M3DVector3f vOut, M3DVector3f vP0, M3DVector3f vP1, M3DVector3f vP2, M3DVector3f vP3, float t) { // Unrolled loop to speed things up a little bit... float t2 = t * t; float t3 = t2 * t; // X vOut[0] = 0.5f * ( ( 2.0f * vP1[0]) + (-vP0[0] + vP2[0]) * t + (2.0f * vP0[0] - 5.0f *vP1[0] + 4.0f * vP2[0] - vP3[0]) * t2 + (-vP0[0] + 3.0f*vP1[0] - 3.0f *vP2[0] + vP3[0]) * t3); // Y vOut[1] = 0.5f * ( ( 2.0f * vP1[1]) + (-vP0[1] + vP2[1]) * t + (2.0f * vP0[1] - 5.0f *vP1[1] + 4.0f * vP2[1] - vP3[1]) * t2 + (-vP0[1] + 3.0f*vP1[1] - 3.0f *vP2[1] + vP3[1]) * t3); // Z vOut[2] = 0.5f * ( ( 2.0f * vP1[2]) + (-vP0[2] + vP2[2]) * t + (2.0f * vP0[2] - 5.0f *vP1[2] + 4.0f * vP2[2] - vP3[2]) * t2 + (-vP0[2] + 3.0f*vP1[2] - 3.0f *vP2[2] + vP3[2]) * t3); } ////////////////////////////////////////////////////////////////////////////////////////////////// // This function does a three dimensional Catmull-Rom curve interpolation. Pass four points, and a // floating point number between 0.0 and 1.0. The curve is interpolated between the middle two points. // Coded by RSW // http://www.mvps.org/directx/articles/catmull/ void m3dCatmullRom3(M3DVector3d vOut, M3DVector3d vP0, M3DVector3d vP1, M3DVector3d vP2, M3DVector3d vP3, double t) { // Unrolled loop to speed things up a little bit... double t2 = t * t; double t3 = t2 * t; // X vOut[0] = 0.5 * ( ( 2.0 * vP1[0]) + (-vP0[0] + vP2[0]) * t + (2.0 * vP0[0] - 5.0 *vP1[0] + 4.0 * vP2[0] - vP3[0]) * t2 + (-vP0[0] + 3.0*vP1[0] - 3.0 *vP2[0] + vP3[0]) * t3); // Y vOut[1] = 0.5 * ( ( 2.0 * vP1[1]) + (-vP0[1] + vP2[1]) * t + (2.0 * vP0[1] - 5.0 *vP1[1] + 4.0 * vP2[1] - vP3[1]) * t2 + (-vP0[1] + 3*vP1[1] - 3.0 *vP2[1] + vP3[1]) * t3); // Z vOut[2] = 0.5 * ( ( 2.0 * vP1[2]) + (-vP0[2] + vP2[2]) * t + (2.0 * vP0[2] - 5.0 *vP1[2] + 4.0 * vP2[2] - vP3[2]) * t2 + (-vP0[2] + 3.0*vP1[2] - 3.0 *vP2[2] + vP3[2]) * t3); } /////////////////////////////////////////////////////////////////////////////// // Determine if the ray (starting at point) intersects the sphere centered at // sphereCenter with radius sphereRadius // Return value is < 0 if the ray does not intersect // Return value is 0.0 if ray is tangent // Positive value is distance to the intersection point // Algorithm from "3D Math Primer for Graphics and Game Development" double m3dRaySphereTest(const M3DVector3d point, const M3DVector3d ray, const M3DVector3d sphereCenter, double sphereRadius) { //m3dNormalizeVector(ray); // Make sure ray is unit length M3DVector3d rayToCenter; // Ray to center of sphere rayToCenter[0] = sphereCenter[0] - point[0]; rayToCenter[1] = sphereCenter[1] - point[1]; rayToCenter[2] = sphereCenter[2] - point[2]; // Project rayToCenter on ray to test double a = m3dDotProduct(rayToCenter, ray); // Distance to center of sphere double distance2 = m3dDotProduct(rayToCenter, rayToCenter); // Or length double dRet = (sphereRadius * sphereRadius) - distance2 + (a*a); if (dRet > 0.0) // Return distance to intersection dRet = a - sqrt(dRet); return dRet; } /////////////////////////////////////////////////////////////////////////////// // Determine if the ray (starting at point) intersects the sphere centered at // ditto above, but uses floating point math float m3dRaySphereTest(const M3DVector3f point, const M3DVector3f ray, const M3DVector3f sphereCenter, float sphereRadius) { //m3dNormalizeVectorf(ray); // Make sure ray is unit length M3DVector3f rayToCenter; // Ray to center of sphere rayToCenter[0] = sphereCenter[0] - point[0]; rayToCenter[1] = sphereCenter[1] - point[1]; rayToCenter[2] = sphereCenter[2] - point[2]; // Project rayToCenter on ray to test float a = m3dDotProduct(rayToCenter, ray); // Distance to center of sphere float distance2 = m3dDotProduct(rayToCenter, rayToCenter); // Or length float dRet = (sphereRadius * sphereRadius) - distance2 + (a*a); if (dRet > 0.0) // Return distance to intersection dRet = a - sqrtf(dRet); return dRet; } /////////////////////////////////////////////////////////////////////////////////////////////////// // Calculate the tangent basis for a triangle on the surface of a model // This vector is needed for most normal mapping shaders void m3dCalculateTangentBasis(const M3DVector3f vTriangle[3], const M3DVector2f vTexCoords[3], const M3DVector3f N, M3DVector3f vTangent) { M3DVector3f dv2v1, dv3v1; float dc2c1t, dc2c1b, dc3c1t, dc3c1b; float M; m3dSubtractVectors3(dv2v1, vTriangle[1], vTriangle[0]); m3dSubtractVectors3(dv3v1, vTriangle[2], vTriangle[0]); dc2c1t = vTexCoords[1][0] - vTexCoords[0][0]; dc2c1b = vTexCoords[1][1] - vTexCoords[0][1]; dc3c1t = vTexCoords[2][0] - vTexCoords[0][0]; dc3c1b = vTexCoords[2][1] - vTexCoords[0][1]; M = (dc2c1t * dc3c1b) - (dc3c1t * dc2c1b); M = 1.0f / M; m3dScaleVector3(dv2v1, dc3c1b); m3dScaleVector3(dv3v1, dc2c1b); m3dSubtractVectors3(vTangent, dv2v1, dv3v1); m3dScaleVector3(vTangent, M); // This potentially changes the direction of the vector m3dNormalizeVector(vTangent); M3DVector3f B; m3dCrossProduct(B, N, vTangent); m3dCrossProduct(vTangent, B, N); m3dNormalizeVector(vTangent); } //////////////////////////////////////////////////////////////////////////// // Smoothly step between 0 and 1 between edge1 and edge 2 double m3dSmoothStep(double edge1, double edge2, double x) { double t; t = (x - edge1) / (edge2 - edge1); if (t > 1.0) t = 1.0; if (t < 0.0) t = 0.0f; return t * t * ( 3.0 - 2.0 * t); } //////////////////////////////////////////////////////////////////////////// // Smoothly step between 0 and 1 between edge1 and edge 2 float m3dSmoothStep(float edge1, float edge2, float x) { float t; t = (x - edge1) / (edge2 - edge1); if (t > 1.0f) t = 1.0f; if (t < 0.0) t = 0.0f; return t * t * ( 3.0f - 2.0f * t); } /////////////////////////////////////////////////////////////////////////// // Creae a projection to "squish" an object into the plane. // Use m3dGetPlaneEquationf(planeEq, point1, point2, point3); // to get a plane equation. void m3dMakePlanarShadowMatrix(M3DMatrix44f proj, const M3DVector4f planeEq, const M3DVector3f vLightPos) { // These just make the code below easier to read. They will be // removed by the optimizer. float a = planeEq[0]; float b = planeEq[1]; float c = planeEq[2]; float d = planeEq[3]; float dx = -vLightPos[0]; float dy = -vLightPos[1]; float dz = -vLightPos[2]; // Now build the projection matrix proj[0] = b * dy + c * dz; proj[1] = -a * dy; proj[2] = -a * dz; proj[3] = 0.0; proj[4] = -b * dx; proj[5] = a * dx + c * dz; proj[6] = -b * dz; proj[7] = 0.0; proj[8] = -c * dx; proj[9] = -c * dy; proj[10] = a * dx + b * dy; proj[11] = 0.0; proj[12] = -d * dx; proj[13] = -d * dy; proj[14] = -d * dz; proj[15] = a * dx + b * dy + c * dz; // Shadow matrix ready } /////////////////////////////////////////////////////////////////////////// // Creae a projection to "squish" an object into the plane. // Use m3dGetPlaneEquationd(planeEq, point1, point2, point3); // to get a plane equation. void m3dMakePlanarShadowMatrix(M3DMatrix44d proj, const M3DVector4d planeEq, const M3DVector3f vLightPos) { // These just make the code below easier to read. They will be // removed by the optimizer. double a = planeEq[0]; double b = planeEq[1]; double c = planeEq[2]; double d = planeEq[3]; double dx = -vLightPos[0]; double dy = -vLightPos[1]; double dz = -vLightPos[2]; // Now build the projection matrix proj[0] = b * dy + c * dz; proj[1] = -a * dy; proj[2] = -a * dz; proj[3] = 0.0; proj[4] = -b * dx; proj[5] = a * dx + c * dz; proj[6] = -b * dz; proj[7] = 0.0; proj[8] = -c * dx; proj[9] = -c * dy; proj[10] = a * dx + b * dy; proj[11] = 0.0; proj[12] = -d * dx; proj[13] = -d * dy; proj[14] = -d * dz; proj[15] = a * dx + b * dy + c * dz; // Shadow matrix ready } ///////////////////////////////////////////////////////////////////////////// // I want to know the point on a ray, closest to another given point in space. // As a bonus, return the distance squared of the two points. // In: vRayOrigin is the origin of the ray. // In: vUnitRayDir is the unit vector of the ray // In: vPointInSpace is the point in space // Out: vPointOnRay is the poing on the ray closest to vPointInSpace // Return: The square of the distance to the ray double m3dClosestPointOnRay(M3DVector3d vPointOnRay, const M3DVector3d vRayOrigin, const M3DVector3d vUnitRayDir, const M3DVector3d vPointInSpace) { M3DVector3d v; m3dSubtractVectors3(v, vPointInSpace, vRayOrigin); double t = m3dDotProduct(vUnitRayDir, v); // This is the point on the ray vPointOnRay[0] = vRayOrigin[0] + (t * vUnitRayDir[0]); vPointOnRay[1] = vRayOrigin[1] + (t * vUnitRayDir[1]); vPointOnRay[2] = vRayOrigin[2] + (t * vUnitRayDir[2]); return m3dGetDistanceSquared(vPointOnRay, vPointInSpace); } // Ditto above... but with floats float m3dClosestPointOnRay(M3DVector3f vPointOnRay, const M3DVector3f vRayOrigin, const M3DVector3f vUnitRayDir, const M3DVector3f vPointInSpace) { M3DVector3f v; m3dSubtractVectors3(v, vPointInSpace, vRayOrigin); float t = m3dDotProduct(vUnitRayDir, v); // This is the point on the ray vPointOnRay[0] = vRayOrigin[0] + (t * vUnitRayDir[0]); vPointOnRay[1] = vRayOrigin[1] + (t * vUnitRayDir[1]); vPointOnRay[2] = vRayOrigin[2] + (t * vUnitRayDir[2]); return m3dGetDistanceSquared(vPointOnRay, vPointInSpace); }