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Diffstat (limited to 'source/blender/blenlib/intern/arithb.c')
| -rw-r--r-- | source/blender/blenlib/intern/arithb.c | 3672 |
1 files changed, 3672 insertions, 0 deletions
diff --git a/source/blender/blenlib/intern/arithb.c b/source/blender/blenlib/intern/arithb.c new file mode 100644 index 00000000000..721df3a1a0c --- /dev/null +++ b/source/blender/blenlib/intern/arithb.c @@ -0,0 +1,3672 @@ +/* arithb.c + * + * simple math for blender code + * + * sort of cleaned up mar-01 nzc + * + * $Id$ + * + * ***** BEGIN GPL/BL DUAL LICENSE BLOCK ***** + * + * This program is free software; you can redistribute it and/or + * modify it under the terms of the GNU General Public License + * as published by the Free Software Foundation; either version 2 + * of the License, or (at your option) any later version. The Blender + * Foundation also sells licenses for use in proprietary software under + * the Blender License. See http://www.blender.org/BL/ for information + * about this. + * + * This program is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU General Public License for more details. + * + * You should have received a copy of the GNU General Public License + * along with this program; if not, write to the Free Software Foundation, + * Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + * + * The Original Code is Copyright (C) 2001-2002 by NaN Holding BV. + * All rights reserved. + * + * The Original Code is: all of this file. + * + * Contributor(s): none yet. + * + * ***** END GPL/BL DUAL LICENSE BLOCK ***** + */ + +/* ************************ FUNKTIES **************************** */ + +#include <math.h> +#include <sys/types.h> +#include <string.h> +#include <float.h> + +#ifdef HAVE_CONFIG_H +#include <config.h> +#endif + +#if defined(__sun__) || defined( __sun ) || defined (__sparc) || defined (__sparc__) +#include <strings.h> +#endif + +#if !defined(__sgi) && !defined(WIN32) +#include <sys/time.h> +#include <unistd.h> +#endif + +#include <stdio.h> +#include "BLI_arithb.h" + +/* A few small defines. Keep'em local! */ +#define SMALL_NUMBER 1.e-8 +#define ABS(x) ((x) < 0 ? -(x) : (x)) +#define SWAP(type, a, b) { type sw_ap; sw_ap=(a); (a)=(b); (b)=sw_ap; } + + +#if defined(WIN32) || defined(__APPLE__) +#include <stdlib.h> +#define M_PI 3.14159265358979323846 +#define M_SQRT2 1.41421356237309504880 + +#endif /* defined(WIN32) || defined(__APPLE__) */ + + +float saacos(float fac) +{ + if(fac<= -1.0f) return (float)M_PI; + else if(fac>=1.0f) return 0.0; + else return (float)acos(fac); +} + +float saasin(float fac) +{ + if(fac<= -1.0f) return (float)-M_PI/2.0f; + else if(fac>=1.0f) return (float)M_PI/2.0f; + else return (float)asin(fac); +} + +float sasqrt(float fac) +{ + if(fac<=0.0) return 0.0; + return (float)sqrt(fac); +} + +float Normalize(float *n) +{ + float d; + + d= n[0]*n[0]+n[1]*n[1]+n[2]*n[2]; + /* A larger value causes normalize errors in a scaled down models with camera xtreme close */ + if(d>1.0e-35F) { + d= (float)sqrt(d); + + n[0]/=d; + n[1]/=d; + n[2]/=d; + } else { + n[0]=n[1]=n[2]= 0.0; + d= 0.0; + } + return d; +} + +void Crossf(float *c, float *a, float *b) +{ + c[0] = a[1] * b[2] - a[2] * b[1]; + c[1] = a[2] * b[0] - a[0] * b[2]; + c[2] = a[0] * b[1] - a[1] * b[0]; +} + +/* Inpf returns the dot product, also called the scalar product and inner product */ +float Inpf( float *v1, float *v2) +{ + return v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2]; +} + +/* Project v1 on v2 */ +void Projf(float *c, float *v1, float *v2) +{ + float mul; + mul = Inpf(v1, v2) / Inpf(v2, v2); + + c[0] = mul * v2[0]; + c[1] = mul * v2[1]; + c[2] = mul * v2[2]; +} + +void Mat3Transp(float mat[][3]) +{ + float t; + + t = mat[0][1] ; + mat[0][1] = mat[1][0] ; + mat[1][0] = t; + t = mat[0][2] ; + mat[0][2] = mat[2][0] ; + mat[2][0] = t; + t = mat[1][2] ; + mat[1][2] = mat[2][1] ; + mat[2][1] = t; +} + +void Mat4Transp(float mat[][4]) +{ + float t; + + t = mat[0][1] ; + mat[0][1] = mat[1][0] ; + mat[1][0] = t; + t = mat[0][2] ; + mat[0][2] = mat[2][0] ; + mat[2][0] = t; + t = mat[0][3] ; + mat[0][3] = mat[3][0] ; + mat[3][0] = t; + + t = mat[1][2] ; + mat[1][2] = mat[2][1] ; + mat[2][1] = t; + t = mat[1][3] ; + mat[1][3] = mat[3][1] ; + mat[3][1] = t; + + t = mat[2][3] ; + mat[2][3] = mat[3][2] ; + mat[3][2] = t; +} + + +/* + * invertmat - + * computes the inverse of mat and puts it in inverse. Returns + * TRUE on success (i.e. can always find a pivot) and FALSE on failure. + * Uses Gaussian Elimination with partial (maximal column) pivoting. + * + * Mark Segal - 1992 + */ + +int Mat4Invert(float inverse[][4], float mat[][4]) +{ + int i, j, k; + double temp; + float tempmat[4][4]; + float max; + int maxj; + + /* Set inverse to identity */ + for (i=0; i<4; i++) + for (j=0; j<4; j++) + inverse[i][j] = 0; + for (i=0; i<4; i++) + inverse[i][i] = 1; + + /* Copy original matrix so we don't mess it up */ + for(i = 0; i < 4; i++) + for(j = 0; j <4; j++) + tempmat[i][j] = mat[i][j]; + + for(i = 0; i < 4; i++) { + /* Look for row with max pivot */ + max = ABS(tempmat[i][i]); + maxj = i; + for(j = i + 1; j < 4; j++) { + if(ABS(tempmat[j][i]) > max) { + max = ABS(tempmat[j][i]); + maxj = j; + } + } + /* Swap rows if necessary */ + if (maxj != i) { + for( k = 0; k < 4; k++) { + SWAP(float, tempmat[i][k], tempmat[maxj][k]); + SWAP(float, inverse[i][k], inverse[maxj][k]); + } + } + + temp = tempmat[i][i]; + if (temp == 0) + return 0; /* No non-zero pivot */ + for(k = 0; k < 4; k++) { + tempmat[i][k] = (float)(tempmat[i][k]/temp); + inverse[i][k] = (float)(inverse[i][k]/temp); + } + for(j = 0; j < 4; j++) { + if(j != i) { + temp = tempmat[j][i]; + for(k = 0; k < 4; k++) { + tempmat[j][k] -= (float)(tempmat[i][k]*temp); + inverse[j][k] -= (float)(inverse[i][k]*temp); + } + } + } + } + return 1; +} +#ifdef TEST_ACTIVE +void Mat4InvertSimp(float inverse[][4], float mat[][4]) +{ + /* only for Matrices that have a rotation */ + /* based at GG IV pag 205 */ + float scale; + + scale= mat[0][0]*mat[0][0] + mat[1][0]*mat[1][0] + mat[2][0]*mat[2][0]; + if(scale==0.0) return; + + scale= 1.0/scale; + + /* transpose and scale */ + inverse[0][0]= scale*mat[0][0]; + inverse[1][0]= scale*mat[0][1]; + inverse[2][0]= scale*mat[0][2]; + inverse[0][1]= scale*mat[1][0]; + inverse[1][1]= scale*mat[1][1]; + inverse[2][1]= scale*mat[1][2]; + inverse[0][2]= scale*mat[2][0]; + inverse[1][2]= scale*mat[2][1]; + inverse[2][2]= scale*mat[2][2]; + + inverse[3][0]= -(inverse[0][0]*mat[3][0] + inverse[1][0]*mat[3][1] + inverse[2][0]*mat[3][2]); + inverse[3][1]= -(inverse[0][1]*mat[3][0] + inverse[1][1]*mat[3][1] + inverse[2][1]*mat[3][2]); + inverse[3][2]= -(inverse[0][2]*mat[3][0] + inverse[1][2]*mat[3][1] + inverse[2][2]*mat[3][2]); + + inverse[0][3]= inverse[1][3]= inverse[2][3]= 0.0; + inverse[3][3]= 1.0; +} +#endif +/* struct Matrix4; */ + +#ifdef TEST_ACTIVE +/* this seems to be unused.. */ + +void Mat4Inv(float *m1, float *m2) +{ + +/* This gets me into trouble: */ + float mat1[3][3], mat2[3][3]; + +/* void Mat3Inv(); */ +/* void Mat3CpyMat4(); */ +/* void Mat4CpyMat3(); */ + + Mat3CpyMat4((float*)mat2,m2); + Mat3Inv((float*)mat1, (float*) mat2); + Mat4CpyMat3(m1, mat1); + +} +#endif + + +float Det2x2(float a,float b,float c,float d) +{ + + return a*d - b*c; +} + + + +float Det3x3(float a1, float a2, float a3, + float b1, float b2, float b3, + float c1, float c2, float c3 ) +{ + float ans; + + ans = a1 * Det2x2( b2, b3, c2, c3 ) + - b1 * Det2x2( a2, a3, c2, c3 ) + + c1 * Det2x2( a2, a3, b2, b3 ); + + return ans; +} + +float Det4x4(float m[][4]) +{ + float ans; + float a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4,d1,d2,d3,d4; + + a1= m[0][0]; + b1= m[0][1]; + c1= m[0][2]; + d1= m[0][3]; + + a2= m[1][0]; + b2= m[1][1]; + c2= m[1][2]; + d2= m[1][3]; + + a3= m[2][0]; + b3= m[2][1]; + c3= m[2][2]; + d3= m[2][3]; + + a4= m[3][0]; + b4= m[3][1]; + c4= m[3][2]; + d4= m[3][3]; + + ans = a1 * Det3x3( b2, b3, b4, c2, c3, c4, d2, d3, d4) + - b1 * Det3x3( a2, a3, a4, c2, c3, c4, d2, d3, d4) + + c1 * Det3x3( a2, a3, a4, b2, b3, b4, d2, d3, d4) + - d1 * Det3x3( a2, a3, a4, b2, b3, b4, c2, c3, c4); + + return ans; +} + + +void Mat4Adj(float out[][4], float in[][4]) /* out = ADJ(in) */ +{ + float a1, a2, a3, a4, b1, b2, b3, b4; + float c1, c2, c3, c4, d1, d2, d3, d4; + + a1= in[0][0]; + b1= in[0][1]; + c1= in[0][2]; + d1= in[0][3]; + + a2= in[1][0]; + b2= in[1][1]; + c2= in[1][2]; + d2= in[1][3]; + + a3= in[2][0]; + b3= in[2][1]; + c3= in[2][2]; + d3= in[2][3]; + + a4= in[3][0]; + b4= in[3][1]; + c4= in[3][2]; + d4= in[3][3]; + + + out[0][0] = Det3x3( b2, b3, b4, c2, c3, c4, d2, d3, d4); + out[1][0] = - Det3x3( a2, a3, a4, c2, c3, c4, d2, d3, d4); + out[2][0] = Det3x3( a2, a3, a4, b2, b3, b4, d2, d3, d4); + out[3][0] = - Det3x3( a2, a3, a4, b2, b3, b4, c2, c3, c4); + + out[0][1] = - Det3x3( b1, b3, b4, c1, c3, c4, d1, d3, d4); + out[1][1] = Det3x3( a1, a3, a4, c1, c3, c4, d1, d3, d4); + out[2][1] = - Det3x3( a1, a3, a4, b1, b3, b4, d1, d3, d4); + out[3][1] = Det3x3( a1, a3, a4, b1, b3, b4, c1, c3, c4); + + out[0][2] = Det3x3( b1, b2, b4, c1, c2, c4, d1, d2, d4); + out[1][2] = - Det3x3( a1, a2, a4, c1, c2, c4, d1, d2, d4); + out[2][2] = Det3x3( a1, a2, a4, b1, b2, b4, d1, d2, d4); + out[3][2] = - Det3x3( a1, a2, a4, b1, b2, b4, c1, c2, c4); + + out[0][3] = - Det3x3( b1, b2, b3, c1, c2, c3, d1, d2, d3); + out[1][3] = Det3x3( a1, a2, a3, c1, c2, c3, d1, d2, d3); + out[2][3] = - Det3x3( a1, a2, a3, b1, b2, b3, d1, d2, d3); + out[3][3] = Det3x3( a1, a2, a3, b1, b2, b3, c1, c2, c3); +} + +void Mat4InvGG(float out[][4], float in[][4]) /* from Graphic Gems I, out= INV(in) */ +{ + int i, j; + float det; + + /* calculate the adjoint matrix */ + + Mat4Adj(out,in); + + det = Det4x4(out); + + if ( fabs( det ) < SMALL_NUMBER) { + return; + } + + /* scale the adjoint matrix to get the inverse */ + + for (i=0; i<4; i++) + for(j=0; j<4; j++) + out[i][j] = out[i][j] / det; + + /* the last factor is not always 1. For that reason an extra division should be implemented? */ +} + + +void Mat3Inv(float m1[][3], float m2[][3]) +{ + short a,b; + float det; + + /* calc adjoint */ + Mat3Adj(m1,m2); + + /* then determinant old matrix! */ + det= m2[0][0]* (m2[1][1]*m2[2][2] - m2[1][2]*m2[2][1]) + -m2[1][0]* (m2[0][1]*m2[2][2] - m2[0][2]*m2[2][1]) + +m2[2][0]* (m2[0][1]*m2[1][2] - m2[0][2]*m2[1][1]); + + if(det==0) det=1; + det= 1/det; + for(a=0;a<3;a++) { + for(b=0;b<3;b++) { + m1[a][b]*=det; + } + } +} + +void Mat3Adj(float m1[][3], float m[][3]) +{ + m1[0][0]=m[1][1]*m[2][2]-m[1][2]*m[2][1]; + m1[0][1]= -m[0][1]*m[2][2]+m[0][2]*m[2][1]; + m1[0][2]=m[0][1]*m[1][2]-m[0][2]*m[1][1]; + + m1[1][0]= -m[1][0]*m[2][2]+m[1][2]*m[2][0]; + m1[1][1]=m[0][0]*m[2][2]-m[0][2]*m[2][0]; + m1[1][2]= -m[0][0]*m[1][2]+m[0][2]*m[1][0]; + + m1[2][0]=m[1][0]*m[2][1]-m[1][1]*m[2][0]; + m1[2][1]= -m[0][0]*m[2][1]+m[0][1]*m[2][0]; + m1[2][2]=m[0][0]*m[1][1]-m[0][1]*m[1][0]; +} + +void Mat4MulMat4(float m1[][4], float m2[][4], float m3[][4]) +{ + /* matrix product: m1[j][k] = m2[j][i].m3[i][k] */ + + m1[0][0] = m2[0][0]*m3[0][0] + m2[0][1]*m3[1][0] + m2[0][2]*m3[2][0] + m2[0][3]*m3[3][0]; + m1[0][1] = m2[0][0]*m3[0][1] + m2[0][1]*m3[1][1] + m2[0][2]*m3[2][1] + m2[0][3]*m3[3][1]; + m1[0][2] = m2[0][0]*m3[0][2] + m2[0][1]*m3[1][2] + m2[0][2]*m3[2][2] + m2[0][3]*m3[3][2]; + m1[0][3] = m2[0][0]*m3[0][3] + m2[0][1]*m3[1][3] + m2[0][2]*m3[2][3] + m2[0][3]*m3[3][3]; + + m1[1][0] = m2[1][0]*m3[0][0] + m2[1][1]*m3[1][0] + m2[1][2]*m3[2][0] + m2[1][3]*m3[3][0]; + m1[1][1] = m2[1][0]*m3[0][1] + m2[1][1]*m3[1][1] + m2[1][2]*m3[2][1] + m2[1][3]*m3[3][1]; + m1[1][2] = m2[1][0]*m3[0][2] + m2[1][1]*m3[1][2] + m2[1][2]*m3[2][2] + m2[1][3]*m3[3][2]; + m1[1][3] = m2[1][0]*m3[0][3] + m2[1][1]*m3[1][3] + m2[1][2]*m3[2][3] + m2[1][3]*m3[3][3]; + + m1[2][0] = m2[2][0]*m3[0][0] + m2[2][1]*m3[1][0] + m2[2][2]*m3[2][0] + m2[2][3]*m3[3][0]; + m1[2][1] = m2[2][0]*m3[0][1] + m2[2][1]*m3[1][1] + m2[2][2]*m3[2][1] + m2[2][3]*m3[3][1]; + m1[2][2] = m2[2][0]*m3[0][2] + m2[2][1]*m3[1][2] + m2[2][2]*m3[2][2] + m2[2][3]*m3[3][2]; + m1[2][3] = m2[2][0]*m3[0][3] + m2[2][1]*m3[1][3] + m2[2][2]*m3[2][3] + m2[2][3]*m3[3][3]; + + m1[3][0] = m2[3][0]*m3[0][0] + m2[3][1]*m3[1][0] + m2[3][2]*m3[2][0] + m2[3][3]*m3[3][0]; + m1[3][1] = m2[3][0]*m3[0][1] + m2[3][1]*m3[1][1] + m2[3][2]*m3[2][1] + m2[3][3]*m3[3][1]; + m1[3][2] = m2[3][0]*m3[0][2] + m2[3][1]*m3[1][2] + m2[3][2]*m3[2][2] + m2[3][3]*m3[3][2]; + m1[3][3] = m2[3][0]*m3[0][3] + m2[3][1]*m3[1][3] + m2[3][2]*m3[2][3] + m2[3][3]*m3[3][3]; + +} +#ifdef TEST_ACTIVE +void subMat4MulMat4(float *m1, float *m2, float *m3) +{ + + m1[0]= m2[0]*m3[0] + m2[1]*m3[4] + m2[2]*m3[8]; + m1[1]= m2[0]*m3[1] + m2[1]*m3[5] + m2[2]*m3[9]; + m1[2]= m2[0]*m3[2] + m2[1]*m3[6] + m2[2]*m3[10]; + m1[3]= m2[0]*m3[3] + m2[1]*m3[7] + m2[2]*m3[11] + m2[3]; + m1+=4; + m2+=4; + m1[0]= m2[0]*m3[0] + m2[1]*m3[4] + m2[2]*m3[8]; + m1[1]= m2[0]*m3[1] + m2[1]*m3[5] + m2[2]*m3[9]; + m1[2]= m2[0]*m3[2] + m2[1]*m3[6] + m2[2]*m3[10]; + m1[3]= m2[0]*m3[3] + m2[1]*m3[7] + m2[2]*m3[11] + m2[3]; + m1+=4; + m2+=4; + m1[0]= m2[0]*m3[0] + m2[1]*m3[4] + m2[2]*m3[8]; + m1[1]= m2[0]*m3[1] + m2[1]*m3[5] + m2[2]*m3[9]; + m1[2]= m2[0]*m3[2] + m2[1]*m3[6] + m2[2]*m3[10]; + m1[3]= m2[0]*m3[3] + m2[1]*m3[7] + m2[2]*m3[11] + m2[3]; +} +#endif + +#ifndef TEST_ACTIVE +void Mat3MulMat3(float m1[][3], float m3[][3], float m2[][3]) +#else +void Mat3MulMat3(float *m1, float *m3, float *m2) +#endif +{ + /* m1[i][j] = m2[i][k]*m3[k][j], args are flipped! */ +#ifndef TEST_ACTIVE + m1[0][0]= m2[0][0]*m3[0][0] + m2[0][1]*m3[1][0] + m2[0][2]*m3[2][0]; + m1[0][1]= m2[0][0]*m3[0][1] + m2[0][1]*m3[1][1] + m2[0][2]*m3[2][1]; + m1[0][2]= m2[0][0]*m3[0][2] + m2[0][1]*m3[1][2] + m2[0][2]*m3[2][2]; + + m1[1][0]= m2[1][0]*m3[0][0] + m2[1][1]*m3[1][0] + m2[1][2]*m3[2][0]; + m1[1][1]= m2[1][0]*m3[0][1] + m2[1][1]*m3[1][1] + m2[1][2]*m3[2][1]; + m1[1][2]= m2[1][0]*m3[0][2] + m2[1][1]*m3[1][2] + m2[1][2]*m3[2][2]; + + m1[2][0]= m2[2][0]*m3[0][0] + m2[2][1]*m3[1][0] + m2[2][2]*m3[2][0]; + m1[2][1]= m2[2][0]*m3[0][1] + m2[2][1]*m3[1][1] + m2[2][2]*m3[2][1]; + m1[2][2]= m2[2][0]*m3[0][2] + m2[2][1]*m3[1][2] + m2[2][2]*m3[2][2]; +#else + m1[0]= m2[0]*m3[0] + m2[1]*m3[3] + m2[2]*m3[6]; + m1[1]= m2[0]*m3[1] + m2[1]*m3[4] + m2[2]*m3[7]; + m1[2]= m2[0]*m3[2] + m2[1]*m3[5] + m2[2]*m3[8]; + m1+=3; + m2+=3; + m1[0]= m2[0]*m3[0] + m2[1]*m3[3] + m2[2]*m3[6]; + m1[1]= m2[0]*m3[1] + m2[1]*m3[4] + m2[2]*m3[7]; + m1[2]= m2[0]*m3[2] + m2[1]*m3[5] + m2[2]*m3[8]; + m1+=3; + m2+=3; + m1[0]= m2[0]*m3[0] + m2[1]*m3[3] + m2[2]*m3[6]; + m1[1]= m2[0]*m3[1] + m2[1]*m3[4] + m2[2]*m3[7]; + m1[2]= m2[0]*m3[2] + m2[1]*m3[5] + m2[2]*m3[8]; +#endif +} /* end of void Mat3MulMat3(float m1[][3], float m3[][3], float m2[][3]) */ + +void Mat4MulMat43(float (*m1)[4], float (*m3)[4], float (*m2)[3]) +{ + m1[0][0]= m2[0][0]*m3[0][0] + m2[0][1]*m3[1][0] + m2[0][2]*m3[2][0]; + m1[0][1]= m2[0][0]*m3[0][1] + m2[0][1]*m3[1][1] + m2[0][2]*m3[2][1]; + m1[0][2]= m2[0][0]*m3[0][2] + m2[0][1]*m3[1][2] + m2[0][2]*m3[2][2]; + m1[1][0]= m2[1][0]*m3[0][0] + m2[1][1]*m3[1][0] + m2[1][2]*m3[2][0]; + m1[1][1]= m2[1][0]*m3[0][1] + m2[1][1]*m3[1][1] + m2[1][2]*m3[2][1]; + m1[1][2]= m2[1][0]*m3[0][2] + m2[1][1]*m3[1][2] + m2[1][2]*m3[2][2]; + m1[2][0]= m2[2][0]*m3[0][0] + m2[2][1]*m3[1][0] + m2[2][2]*m3[2][0]; + m1[2][1]= m2[2][0]*m3[0][1] + m2[2][1]*m3[1][1] + m2[2][2]*m3[2][1]; + m1[2][2]= m2[2][0]*m3[0][2] + m2[2][1]*m3[1][2] + m2[2][2]*m3[2][2]; +} +/* m1 = m2 * m3, ignore the elements on the 4th row/column of m3*/ +void Mat3IsMat3MulMat4(float m1[][3], float m2[][3], float m3[][4]) +{ + /* m1[i][j] = m2[i][k] * m3[k][j] */ + m1[0][0] = m2[0][0] * m3[0][0] + m2[0][1] * m3[1][0] +m2[0][2] * m3[2][0]; + m1[0][1] = m2[0][0] * m3[0][1] + m2[0][1] * m3[1][1] +m2[0][2] * m3[2][1]; + m1[0][2] = m2[0][0] * m3[0][2] + m2[0][1] * m3[1][2] +m2[0][2] * m3[2][2]; + + m1[1][0] = m2[1][0] * m3[0][0] + m2[1][1] * m3[1][0] +m2[1][2] * m3[2][0]; + m1[1][1] = m2[1][0] * m3[0][1] + m2[1][1] * m3[1][1] +m2[1][2] * m3[2][1]; + m1[1][2] = m2[1][0] * m3[0][2] + m2[1][1] * m3[1][2] +m2[1][2] * m3[2][2]; + + m1[2][0] = m2[2][0] * m3[0][0] + m2[2][1] * m3[1][0] +m2[2][2] * m3[2][0]; + m1[2][1] = m2[2][0] * m3[0][1] + m2[2][1] * m3[1][1] +m2[2][2] * m3[2][1]; + m1[2][2] = m2[2][0] * m3[0][2] + m2[2][1] * m3[1][2] +m2[2][2] * m3[2][2]; +} + + + +void Mat4MulMat34(float (*m1)[4], float (*m3)[3], float (*m2)[4]) +{ + m1[0][0]= m2[0][0]*m3[0][0] + m2[0][1]*m3[1][0] + m2[0][2]*m3[2][0]; + m1[0][1]= m2[0][0]*m3[0][1] + m2[0][1]*m3[1][1] + m2[0][2]*m3[2][1]; + m1[0][2]= m2[0][0]*m3[0][2] + m2[0][1]*m3[1][2] + m2[0][2]*m3[2][2]; + m1[1][0]= m2[1][0]*m3[0][0] + m2[1][1]*m3[1][0] + m2[1][2]*m3[2][0]; + m1[1][1]= m2[1][0]*m3[0][1] + m2[1][1]*m3[1][1] + m2[1][2]*m3[2][1]; + m1[1][2]= m2[1][0]*m3[0][2] + m2[1][1]*m3[1][2] + m2[1][2]*m3[2][2]; + m1[2][0]= m2[2][0]*m3[0][0] + m2[2][1]*m3[1][0] + m2[2][2]*m3[2][0]; + m1[2][1]= m2[2][0]*m3[0][1] + m2[2][1]*m3[1][1] + m2[2][2]*m3[2][1]; + m1[2][2]= m2[2][0]*m3[0][2] + m2[2][1]*m3[1][2] + m2[2][2]*m3[2][2]; +} + +void Mat4CpyMat4(float m1[][4], float m2[][4]) +{ + memcpy(m1, m2, 4*4*sizeof(float)); +} + +void Mat4SwapMat4(float *m1, float *m2) +{ + float t; + int i; + + for(i=0;i<16;i++) { + t= *m1; + *m1= *m2; + *m2= t; + m1++; + m2++; + } +} + +typedef float Mat3Row[3]; +typedef float Mat4Row[4]; + +#ifdef TEST_ACTIVE +void Mat3CpyMat4(float *m1p, float *m2p) +#else +void Mat3CpyMat4(float m1[][3], float m2[][4]) +#endif +{ +#ifdef TEST_ACTIVE + int i, j; + Mat3Row *m1= (Mat3Row *)m1p; + Mat4Row *m2= (Mat4Row *)m2p; + for ( i = 0; i++; i < 3) { + for (j = 0; j++; j < 3) { + m1p[3*i + j] = m2p[4*i + j]; + } + } +#endif + m1[0][0]= m2[0][0]; + m1[0][1]= m2[0][1]; + m1[0][2]= m2[0][2]; + + m1[1][0]= m2[1][0]; + m1[1][1]= m2[1][1]; + m1[1][2]= m2[1][2]; + + m1[2][0]= m2[2][0]; + m1[2][1]= m2[2][1]; + m1[2][2]= m2[2][2]; +} + +/* Butched. See .h for comment */ +/* void Mat4CpyMat3(float m1[][4], float m2[][3]) */ +#ifdef TEST_ACTIVE +void Mat4CpyMat3(float* m1, float *m2) +{ + int i; + for (i = 0; i < 3; i++) { + m1[(4*i)] = m2[(3*i)]; + m1[(4*i) + 1]= m2[(3*i) + 1]; + m1[(4*i) + 2]= m2[(3*i) + 2]; + m1[(4*i) + 3]= 0.0; + i++; + } + + m1[12]=m1[13]= m1[14]= 0.0; + m1[15]= 1.0; +} +#else + +void Mat4CpyMat3(float m1[][4], float m2[][3]) /* no clear */ +{ + m1[0][0]= m2[0][0]; + m1[0][1]= m2[0][1]; + m1[0][2]= m2[0][2]; + + m1[1][0]= m2[1][0]; + m1[1][1]= m2[1][1]; + m1[1][2]= m2[1][2]; + + m1[2][0]= m2[2][0]; + m1[2][1]= m2[2][1]; + m1[2][2]= m2[2][2]; + + /* Reevan's Bugfix */ + m1[0][3]=0.0F; + m1[1][3]=0.0F; + m1[2][3]=0.0F; + + m1[3][0]=0.0F; + m1[3][1]=0.0F; + m1[3][2]=0.0F; + m1[3][3]=1.0F; + + +} +#endif + +void Mat3CpyMat3(float m1[][3], float m2[][3]) +{ + /* destination comes first: */ + memcpy(&m1[0], &m2[0], 9*sizeof(float)); +} + +void Mat3MulSerie(float answ[][3], + float m1[][3], float m2[][3], float m3[][3], + float m4[][3], float m5[][3], float m6[][3], + float m7[][3], float m8[][3]) +{ + float temp[3][3]; + + if(m1==0 || m2==0) return; + + + Mat3MulMat3(answ, m2, m1); + if(m3) { + Mat3MulMat3(temp, m3, answ); + if(m4) { + Mat3MulMat3(answ, m4, temp); + if(m5) { + Mat3MulMat3(temp, m5, answ); + if(m6) { + Mat3MulMat3(answ, m6, temp); + if(m7) { + Mat3MulMat3(temp, m7, answ); + if(m8) { + Mat3MulMat3(answ, m8, temp); + } + else Mat3CpyMat3(answ, temp); + } + } + else Mat3CpyMat3(answ, temp); + } + } + else Mat3CpyMat3(answ, temp); + } +} + +void Mat4MulSerie(float answ[][4], float m1[][4], + float m2[][4], float m3[][4], float m4[][4], + float m5[][4], float m6[][4], float m7[][4], + float m8[][4]) +{ + float temp[4][4]; + + if(m1==0 || m2==0) return; + + Mat4MulMat4(answ, m2, m1); + if(m3) { + Mat4MulMat4(temp, m3, answ); + if(m4) { + Mat4MulMat4(answ, m4, temp); + if(m5) { + Mat4MulMat4(temp, m5, answ); + if(m6) { + Mat4MulMat4(answ, m6, temp); + if(m7) { + Mat4MulMat4(temp, m7, answ); + if(m8) { + Mat4MulMat4(answ, m8, temp); + } + else Mat4CpyMat4(answ, temp); + } + } + else Mat4CpyMat4(answ, temp); + } + } + else Mat4CpyMat4(answ, temp); + } +} + +void Mat4BlendMat4(float out[][4], float dst[][4], float src[][4], float srcweight) +{ + float squat[4], dquat[4], fquat[4]; + float ssize[3], dsize[3], fsize[4]; + float sloc[3], dloc[3], floc[3]; + + Mat4ToQuat(dst, dquat); + Mat4ToSize(dst, dsize); + VecCopyf(dloc, dst[3]); + + Mat4ToQuat(src, squat); + Mat4ToSize(src, ssize); + VecCopyf(sloc, src[3]); + + /* do blending */ + VecLerpf(floc, dloc, sloc, srcweight); + QuatInterpol(fquat, dquat, squat, srcweight); + VecLerpf(fsize, dsize, ssize, srcweight); + + /* compose new matrix */ + LocQuatSizeToMat4(out, floc, fquat, fsize); +} + +void Mat4Clr(float *m) +{ + memset(m, 0, 4*4*sizeof(float)); +} + +void Mat3Clr(float *m) +{ + memset(m, 0, 3*3*sizeof(float)); +} + +void Mat4One(float m[][4]) +{ + + m[0][0]= m[1][1]= m[2][2]= m[3][3]= 1.0; + m[0][1]= m[0][2]= m[0][3]= 0.0; + m[1][0]= m[1][2]= m[1][3]= 0.0; + m[2][0]= m[2][1]= m[2][3]= 0.0; + m[3][0]= m[3][1]= m[3][2]= 0.0; +} + +void Mat3One(float m[][3]) +{ + + m[0][0]= m[1][1]= m[2][2]= 1.0; + m[0][1]= m[0][2]= 0.0; + m[1][0]= m[1][2]= 0.0; + m[2][0]= m[2][1]= 0.0; +} + +void Mat4MulVec( float mat[][4], int *vec) +{ + int x,y; + + x=vec[0]; + y=vec[1]; + vec[0]=(int)(x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2] + mat[3][0]); + vec[1]=(int)(x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2] + mat[3][1]); + vec[2]=(int)(x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2] + mat[3][2]); +} + +void Mat4MulVecfl( float mat[][4], float *vec) +{ + float x,y; + + x=vec[0]; + y=vec[1]; + vec[0]=x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2] + mat[3][0]; + vec[1]=x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2] + mat[3][1]; + vec[2]=x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2] + mat[3][2]; +} + +void VecMat4MulVecfl(float *in, float mat[][4], float *vec) +{ + float x,y; + + x=vec[0]; + y=vec[1]; + in[0]= x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2] + mat[3][0]; + in[1]= x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2] + mat[3][1]; + in[2]= x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2] + mat[3][2]; +} + +void Mat4Mul3Vecfl( float mat[][4], float *vec) +{ + float x,y; + + x= vec[0]; + y= vec[1]; + vec[0]= x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2]; + vec[1]= x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2]; + vec[2]= x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2]; +} + +void Mat4MulVec3Project(float mat[][4], float *vec) +{ + float w; + + w = vec[0]*mat[0][3] + vec[1]*mat[1][3] + vec[2]*mat[2][3] + mat[3][3]; + Mat4MulVecfl(mat, vec); + + vec[0] /= w; + vec[1] /= w; + vec[2] /= w; +} + +void Mat4MulVec4fl( float mat[][4], float *vec) +{ + float x,y,z; + + x=vec[0]; + y=vec[1]; + z= vec[2]; + vec[0]=x*mat[0][0] + y*mat[1][0] + z*mat[2][0] + mat[3][0]*vec[3]; + vec[1]=x*mat[0][1] + y*mat[1][1] + z*mat[2][1] + mat[3][1]*vec[3]; + vec[2]=x*mat[0][2] + y*mat[1][2] + z*mat[2][2] + mat[3][2]*vec[3]; + vec[3]=x*mat[0][3] + y*mat[1][3] + z*mat[2][3] + mat[3][3]*vec[3]; +} + +void Mat3MulVec( float mat[][3], int *vec) +{ + int x,y; + + x=vec[0]; + y=vec[1]; + vec[0]= (int)(x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2]); + vec[1]= (int)(x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2]); + vec[2]= (int)(x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2]); +} + +void Mat3MulVecfl( float mat[][3], float *vec) +{ + float x,y; + + x=vec[0]; + y=vec[1]; + vec[0]= x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2]; + vec[1]= x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2]; + vec[2]= x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2]; +} + +void Mat3MulVecd( float mat[][3], double *vec) +{ + double x,y; + + x=vec[0]; + y=vec[1]; + vec[0]= x*mat[0][0] + y*mat[1][0] + mat[2][0]*vec[2]; + vec[1]= x*mat[0][1] + y*mat[1][1] + mat[2][1]*vec[2]; + vec[2]= x*mat[0][2] + y*mat[1][2] + mat[2][2]*vec[2]; +} + +void Mat3TransMulVecfl( float mat[][3], float *vec) +{ + float x,y; + + x=vec[0]; + y=vec[1]; + vec[0]= x*mat[0][0] + y*mat[0][1] + mat[0][2]*vec[2]; + vec[1]= x*mat[1][0] + y*mat[1][1] + mat[1][2]*vec[2]; + vec[2]= x*mat[2][0] + y*mat[2][1] + mat[2][2]*vec[2]; +} + +void Mat3MulFloat(float *m, float f) +{ + int i; + + for(i=0;i<9;i++) m[i]*=f; +} + +void Mat4MulFloat(float *m, float f) +{ + int i; + + for(i=0;i<16;i++) m[i]*=f; /* count to 12: without vector component */ +} + + +void Mat4MulFloat3(float *m, float f) /* only scale component */ +{ + int i,j; + + for(i=0; i<3; i++) { + for(j=0; j<3; j++) { + + m[4*i+j] *= f; + } + } +} + +void Mat3AddMat3(float m1[][3], float m2[][3], float m3[][3]) +{ + int i, j; + + for(i=0;i<3;i++) + for(j=0;j<3;j++) + m1[i][j]= m2[i][j] + m3[i][j]; +} + +void Mat4AddMat4(float m1[][4], float m2[][4], float m3[][4]) +{ + int i, j; + + for(i=0;i<4;i++) + for(j=0;j<4;j++) + m1[i][j]= m2[i][j] + m3[i][j]; +} + +void VecStar(float mat[][3], float *vec) +{ + + mat[0][0]= mat[1][1]= mat[2][2]= 0.0; + mat[0][1]= -vec[2]; + mat[0][2]= vec[1]; + mat[1][0]= vec[2]; + mat[1][2]= -vec[0]; + mat[2][0]= -vec[1]; + mat[2][1]= vec[0]; + +} +#ifdef TEST_ACTIVE +short EenheidsMat(float mat[][3]) +{ + + if(mat[0][0]==1.0 && mat[0][1]==0.0 && mat[0][2]==0.0) + if(mat[1][0]==0.0 && mat[1][1]==1.0 && mat[1][2]==0.0) + if(mat[2][0]==0.0 && mat[2][1]==0.0 && mat[2][2]==1.0) + return 1; + return 0; +} +#endif + +int FloatCompare( float *v1, float *v2, float limit) +{ + + if( fabs(v1[0]-v2[0])<limit ) { + if( fabs(v1[1]-v2[1])<limit ) { + if( fabs(v1[2]-v2[2])<limit ) return 1; + } + } + return 0; +} + +float FloatLerpf( float target, float origin, float fac) +{ + return (fac*target) + (1.0f-fac)*origin; +} + +void printvecf( char *str, float v[3]) +{ + printf("%s: %.3f %.3f %.3f\n", str, v[0], v[1], v[2]); + +} + +void printquat( char *str, float q[4]) +{ + printf("%s: %.3f %.3f %.3f %.3f\n", str, q[0], q[1], q[2], q[3]); + +} + +void printvec4f( char *str, float v[4]) +{ + printf("%s\n", str); + printf("%f %f %f %f\n",v[0],v[1],v[2], v[3]); + printf("\n"); + +} + +void printmatrix4( char *str, float m[][4]) +{ + printf("%s\n", str); + printf("%f %f %f %f\n",m[0][0],m[1][0],m[2][0],m[3][0]); + printf("%f %f %f %f\n",m[0][1],m[1][1],m[2][1],m[3][1]); + printf("%f %f %f %f\n",m[0][2],m[1][2],m[2][2],m[3][2]); + printf("%f %f %f %f\n",m[0][3],m[1][3],m[2][3],m[3][3]); + printf("\n"); + +} + +void printmatrix3( char *str, float m[][3]) +{ + printf("%s\n", str); + printf("%f %f %f\n",m[0][0],m[1][0],m[2][0]); + printf("%f %f %f\n",m[0][1],m[1][1],m[2][1]); + printf("%f %f %f\n",m[0][2],m[1][2],m[2][2]); + printf("\n"); + +} + +/* **************** QUATERNIONS ********** */ + + +void QuatMul(float *q, float *q1, float *q2) +{ + float t0,t1,t2; + + t0= q1[0]*q2[0]-q1[1]*q2[1]-q1[2]*q2[2]-q1[3]*q2[3]; + t1= q1[0]*q2[1]+q1[1]*q2[0]+q1[2]*q2[3]-q1[3]*q2[2]; + t2= q1[0]*q2[2]+q1[2]*q2[0]+q1[3]*q2[1]-q1[1]*q2[3]; + q[3]= q1[0]*q2[3]+q1[3]*q2[0]+q1[1]*q2[2]-q1[2]*q2[1]; + q[0]=t0; + q[1]=t1; + q[2]=t2; +} + +/* Assumes a unit quaternion */ +void QuatMulVecf(float *q, float *v) +{ + float t0, t1, t2; + + t0= -q[1]*v[0]-q[2]*v[1]-q[3]*v[2]; + t1= q[0]*v[0]+q[2]*v[2]-q[3]*v[1]; + t2= q[0]*v[1]+q[3]*v[0]-q[1]*v[2]; + v[2]= q[0]*v[2]+q[1]*v[1]-q[2]*v[0]; + v[0]=t1; + v[1]=t2; + + t1= t0*-q[1]+v[0]*q[0]-v[1]*q[3]+v[2]*q[2]; + t2= t0*-q[2]+v[1]*q[0]-v[2]*q[1]+v[0]*q[3]; + v[2]= t0*-q[3]+v[2]*q[0]-v[0]*q[2]+v[1]*q[1]; + v[0]=t1; + v[1]=t2; +} + +void QuatConj(float *q) +{ + q[1] = -q[1]; + q[2] = -q[2]; + q[3] = -q[3]; +} + +float QuatDot(float *q1, float *q2) +{ + return q1[0]*q2[0] + q1[1]*q2[1] + q1[2]*q2[2] + q1[3]*q2[3]; +} + +void QuatInv(float *q) +{ + float f = QuatDot(q, q); + + if (f == 0.0f) + return; + + QuatConj(q); + QuatMulf(q, 1.0f/f); +} + +void QuatMulf(float *q, float f) +{ + q[0] *= f; + q[1] *= f; + q[2] *= f; + q[3] *= f; +} + +void QuatSub(float *q, float *q1, float *q2) +{ + q2[0]= -q2[0]; + QuatMul(q, q1, q2); + q2[0]= -q2[0]; +} + + +void QuatToMat3( float *q, float m[][3]) +{ + double q0, q1, q2, q3, qda,qdb,qdc,qaa,qab,qac,qbb,qbc,qcc; + + q0= M_SQRT2 * q[0]; + q1= M_SQRT2 * q[1]; + q2= M_SQRT2 * q[2]; + q3= M_SQRT2 * q[3]; + + qda= q0*q1; + qdb= q0*q2; + qdc= q0*q3; + qaa= q1*q1; + qab= q1*q2; + qac= q1*q3; + qbb= q2*q2; + qbc= q2*q3; + qcc= q3*q3; + + m[0][0]= (float)(1.0-qbb-qcc); + m[0][1]= (float)(qdc+qab); + m[0][2]= (float)(-qdb+qac); + + m[1][0]= (float)(-qdc+qab); + m[1][1]= (float)(1.0-qaa-qcc); + m[1][2]= (float)(qda+qbc); + + m[2][0]= (float)(qdb+qac); + m[2][1]= (float)(-qda+qbc); + m[2][2]= (float)(1.0-qaa-qbb); +} + + +void QuatToMat4( float *q, float m[][4]) +{ + double q0, q1, q2, q3, qda,qdb,qdc,qaa,qab,qac,qbb,qbc,qcc; + + q0= M_SQRT2 * q[0]; + q1= M_SQRT2 * q[1]; + q2= M_SQRT2 * q[2]; + q3= M_SQRT2 * q[3]; + + qda= q0*q1; + qdb= q0*q2; + qdc= q0*q3; + qaa= q1*q1; + qab= q1*q2; + qac= q1*q3; + qbb= q2*q2; + qbc= q2*q3; + qcc= q3*q3; + + m[0][0]= (float)(1.0-qbb-qcc); + m[0][1]= (float)(qdc+qab); + m[0][2]= (float)(-qdb+qac); + m[0][3]= 0.0f; + + m[1][0]= (float)(-qdc+qab); + m[1][1]= (float)(1.0-qaa-qcc); + m[1][2]= (float)(qda+qbc); + m[1][3]= 0.0f; + + m[2][0]= (float)(qdb+qac); + m[2][1]= (float)(-qda+qbc); + m[2][2]= (float)(1.0-qaa-qbb); + m[2][3]= 0.0f; + + m[3][0]= m[3][1]= m[3][2]= 0.0f; + m[3][3]= 1.0f; +} + +void Mat3ToQuat( float wmat[][3], float *q) /* from Sig.Proc.85 pag 253 */ +{ + double tr, s; + float mat[3][3]; + + /* work on a copy */ + Mat3CpyMat3(mat, wmat); + Mat3Ortho(mat); /* this is needed AND a NormalQuat in the end */ + + tr= 0.25*(1.0+mat[0][0]+mat[1][1]+mat[2][2]); + + if(tr>FLT_EPSILON) { + s= sqrt( tr); + q[0]= (float)s; + s*= 4.0; + q[1]= (float)((mat[1][2]-mat[2][1])/s); + q[2]= (float)((mat[2][0]-mat[0][2])/s); + q[3]= (float)((mat[0][1]-mat[1][0])/s); + } + else { + q[0]= 0.0f; + s= -0.5*(mat[1][1]+mat[2][2]); + + if(s>FLT_EPSILON) { + s= sqrt(s); + q[1]= (float)s; + q[2]= (float)(mat[0][1]/(2*s)); + q[3]= (float)(mat[0][2]/(2*s)); + } + else { + q[1]= 0.0f; + s= 0.5*(1.0-mat[2][2]); + + if(s>FLT_EPSILON) { + s= sqrt(s); + q[2]= (float)s; + q[3]= (float)(mat[1][2]/(2*s)); + } + else { + q[2]= 0.0f; + q[3]= 1.0f; + } + } + } + NormalQuat(q); +} + +void Mat3ToQuat_is_ok( float wmat[][3], float *q) +{ + float mat[3][3], matr[3][3], matn[3][3], q1[4], q2[4], angle, si, co, nor[3]; + + /* work on a copy */ + Mat3CpyMat3(mat, wmat); + Mat3Ortho(mat); + + /* rotate z-axis of matrix to z-axis */ + + nor[0] = mat[2][1]; /* cross product with (0,0,1) */ + nor[1] = -mat[2][0]; + nor[2] = 0.0; + Normalize(nor); + + co= mat[2][2]; + angle= 0.5f*saacos(co); + + co= (float)cos(angle); + si= (float)sin(angle); + q1[0]= co; + q1[1]= -nor[0]*si; /* negative here, but why? */ + q1[2]= -nor[1]*si; + q1[3]= -nor[2]*si; + + /* rotate back x-axis from mat, using inverse q1 */ + QuatToMat3(q1, matr); + Mat3Inv(matn, matr); + Mat3MulVecfl(matn, mat[0]); + + /* and align x-axes */ + angle= (float)(0.5*atan2(mat[0][1], mat[0][0])); + + co= (float)cos(angle); + si= (float)sin(angle); + q2[0]= co; + q2[1]= 0.0f; + q2[2]= 0.0f; + q2[3]= si; + + QuatMul(q, q1, q2); +} + + +void Mat4ToQuat( float m[][4], float *q) +{ + float mat[3][3]; + + Mat3CpyMat4(mat, m); + Mat3ToQuat(mat, q); + +} + +void QuatOne(float *q) +{ + q[0]= q[2]= q[3]= 0.0; + q[1]= 1.0; +} + +void NormalQuat(float *q) +{ + float len; + + len= (float)sqrt(q[0]*q[0]+q[1]*q[1]+q[2]*q[2]+q[3]*q[3]); + if(len!=0.0) { + q[0]/= len; + q[1]/= len; + q[2]/= len; + q[3]/= len; + } else { + q[1]= 1.0f; + q[0]= q[2]= q[3]= 0.0f; + } +} + +float *vectoquat( float *vec, short axis, short upflag) +{ + static float q1[4]; + float q2[4], nor[3], *fp, mat[3][3], angle, si, co, x2, y2, z2, len1; + + /* first rotate to axis */ + if(axis>2) { + x2= vec[0] ; y2= vec[1] ; z2= vec[2]; + axis-= 3; + } + else { + x2= -vec[0] ; y2= -vec[1] ; z2= -vec[2]; + } + + q1[0]=1.0; + q1[1]=q1[2]=q1[3]= 0.0; + + len1= (float)sqrt(x2*x2+y2*y2+z2*z2); + if(len1 == 0.0) return(q1); + + /* nasty! I need a good routine for this... + * problem is a rotation of an Y axis to the negative Y-axis for example. + */ + + if(axis==0) { /* x-axis */ + nor[0]= 0.0; + nor[1]= -z2; + nor[2]= y2; + + if( fabs(y2)+fabs(z2)<0.0001 ) { + nor[1]= 1.0; + } + + co= x2; + } + else if(axis==1) { /* y-axis */ + nor[0]= z2; + nor[1]= 0.0; + nor[2]= -x2; + + if( fabs(x2)+fabs(z2)<0.0001 ) { + nor[2]= 1.0; + } + + co= y2; + } + else { /* z-axis */ + nor[0]= -y2; + nor[1]= x2; + nor[2]= 0.0; + + if( fabs(x2)+fabs(y2)<0.0001 ) { + nor[0]= 1.0; + } + + co= z2; + } + co/= len1; + + Normalize(nor); + + angle= 0.5f*saacos(co); + si= (float)sin(angle); + q1[0]= (float)cos(angle); + q1[1]= nor[0]*si; + q1[2]= nor[1]*si; + q1[3]= nor[2]*si; + + if(axis!=upflag) { + QuatToMat3(q1, mat); + + fp= mat[2]; + if(axis==0) { + if(upflag==1) angle= (float)(0.5*atan2(fp[2], fp[1])); + else angle= (float)(-0.5*atan2(fp[1], fp[2])); + } + else if(axis==1) { + if(upflag==0) angle= (float)(-0.5*atan2(fp[2], fp[0])); + else angle= (float)(0.5*atan2(fp[0], fp[2])); + } + else { + if(upflag==0) angle= (float)(0.5*atan2(-fp[1], -fp[0])); + else angle= (float)(-0.5*atan2(-fp[0], -fp[1])); + } + + co= (float)cos(angle); + si= (float)(sin(angle)/len1); + q2[0]= co; + q2[1]= x2*si; + q2[2]= y2*si; + q2[3]= z2*si; + + QuatMul(q1,q2,q1); + } + + return(q1); +} + +void VecUpMat3old( float *vec, float mat[][3], short axis) +{ + float inp, up[3]; + short cox = 0, coy = 0, coz = 0; + + /* using different up's is not useful, infact there is no real 'up'! + */ + + up[0]= 0.0; + up[1]= 0.0; + up[2]= 1.0; + + if(axis==0) { + cox= 0; coy= 1; coz= 2; /* Y up Z tr */ + } + if(axis==1) { + cox= 1; coy= 2; coz= 0; /* Z up X tr */ + } + if(axis==2) { + cox= 2; coy= 0; coz= 1; /* X up Y tr */ + } + if(axis==3) { + cox= 0; coy= 2; coz= 1; /* */ + } + if(axis==4) { + cox= 1; coy= 0; coz= 2; /* */ + } + if(axis==5) { + cox= 2; coy= 1; coz= 0; /* Y up X tr */ + } + + mat[coz][0]= vec[0]; + mat[coz][1]= vec[1]; + mat[coz][2]= vec[2]; + Normalize((float *)mat[coz]); + + inp= mat[coz][0]*up[0] + mat[coz][1]*up[1] + mat[coz][2]*up[2]; + mat[coy][0]= up[0] - inp*mat[coz][0]; + mat[coy][1]= up[1] - inp*mat[coz][1]; + mat[coy][2]= up[2] - inp*mat[coz][2]; + + Normalize((float *)mat[coy]); + + Crossf(mat[cox], mat[coy], mat[coz]); + +} + +void VecUpMat3(float *vec, float mat[][3], short axis) +{ + float inp; + short cox = 0, coy = 0, coz = 0; + + /* using different up's is not useful, infact there is no real 'up'! + */ + + if(axis==0) { + cox= 0; coy= 1; coz= 2; /* Y up Z tr */ + } + if(axis==1) { + cox= 1; coy= 2; coz= 0; /* Z up X tr */ + } + if(axis==2) { + cox= 2; coy= 0; coz= 1; /* X up Y tr */ + } + if(axis==3) { + cox= 0; coy= 1; coz= 2; /* Y op -Z tr */ + vec[0]= -vec[0]; + vec[1]= -vec[1]; + vec[2]= -vec[2]; + } + if(axis==4) { + cox= 1; coy= 0; coz= 2; /* */ + } + if(axis==5) { + cox= 2; coy= 1; coz= 0; /* Y up X tr */ + } + + mat[coz][0]= vec[0]; + mat[coz][1]= vec[1]; + mat[coz][2]= vec[2]; + Normalize((float *)mat[coz]); + + inp= mat[coz][2]; + mat[coy][0]= - inp*mat[coz][0]; + mat[coy][1]= - inp*mat[coz][1]; + mat[coy][2]= 1.0f - inp*mat[coz][2]; + + Normalize((float *)mat[coy]); + + Crossf(mat[cox], mat[coy], mat[coz]); + +} + +/* A & M Watt, Advanced animation and rendering techniques, 1992 ACM press */ +void QuatInterpolW(float *, float *, float *, float ); + +void QuatInterpolW(float *result, float *quat1, float *quat2, float t) +{ + float omega, cosom, sinom, sc1, sc2; + + cosom = quat1[0]*quat2[0] + quat1[1]*quat2[1] + quat1[2]*quat2[2] + quat1[3]*quat2[3] ; + + /* rotate around shortest angle */ + if ((1.0 + cosom) > 0.0001) { + + if ((1.0 - cosom) > 0.0001) { + omega = acos(cosom); + sinom = sin(omega); + sc1 = sin((1.0 - t) * omega) / sinom; + sc2 = sin(t * omega) / sinom; + } + else { + sc1 = 1.0 - t; + sc2 = t; + } + result[0] = sc1*quat1[0] + sc2*quat2[0]; + result[1] = sc1*quat1[1] + sc2*quat2[1]; + result[2] = sc1*quat1[2] + sc2*quat2[2]; + result[3] = sc1*quat1[3] + sc2*quat2[3]; + } + else { + result[0] = quat2[3]; + result[1] = -quat2[2]; + result[2] = quat2[1]; + result[3] = -quat2[0]; + + sc1 = sin((1.0 - t)*M_PI_2); + sc2 = sin(t*M_PI_2); + + result[0] = sc1*quat1[0] + sc2*result[0]; + result[1] = sc1*quat1[1] + sc2*result[1]; + result[2] = sc1*quat1[2] + sc2*result[2]; + result[3] = sc1*quat1[3] + sc2*result[3]; + } +} + +void QuatInterpol(float *result, float *quat1, float *quat2, float t) +{ + float quat[4], omega, cosom, sinom, sc1, sc2; + + cosom = quat1[0]*quat2[0] + quat1[1]*quat2[1] + quat1[2]*quat2[2] + quat1[3]*quat2[3] ; + + /* rotate around shortest angle */ + if (cosom < 0.0) { + cosom = -cosom; + quat[0]= -quat1[0]; + quat[1]= -quat1[1]; + quat[2]= -quat1[2]; + quat[3]= -quat1[3]; + } + else { + quat[0]= quat1[0]; + quat[1]= quat1[1]; + quat[2]= quat1[2]; + quat[3]= quat1[3]; + } + + if ((1.0 - cosom) > 0.0001) { + omega = acos(cosom); + sinom = sin(omega); + sc1 = sin((1 - t) * omega) / sinom; + sc2 = sin(t * omega) / sinom; + } else { + sc1= 1.0 - t; + sc2= t; + } + + result[0] = sc1 * quat[0] + sc2 * quat2[0]; + result[1] = sc1 * quat[1] + sc2 * quat2[1]; + result[2] = sc1 * quat[2] + sc2 * quat2[2]; + result[3] = sc1 * quat[3] + sc2 * quat2[3]; +} + +void QuatAdd(float *result, float *quat1, float *quat2, float t) +{ + result[0]= quat1[0] + t*quat2[0]; + result[1]= quat1[1] + t*quat2[1]; + result[2]= quat1[2] + t*quat2[2]; + result[3]= quat1[3] + t*quat2[3]; +} + +void QuatCopy(float *q1, float *q2) +{ + q1[0]= q2[0]; + q1[1]= q2[1]; + q1[2]= q2[2]; + q1[3]= q2[3]; +} + +/* **************** DUAL QUATERNIONS ************** */ + +/* + Conversion routines between (regular quaternion, translation) and + dual quaternion. + + Version 1.0.0, February 7th, 2007 + + Copyright (C) 2006-2007 University of Dublin, Trinity College, All Rights + Reserved + + This software is provided 'as-is', without any express or implied + warranty. In no event will the author(s) be held liable for any damages + arising from the use of this software. + + Permission is granted to anyone to use this software for any purpose, + including commercial applications, and to alter it and redistribute it + freely, subject to the following restrictions: + + 1. The origin of this software must not be misrepresented; you must not + claim that you wrote the original software. If you use this software + in a product, an acknowledgment in the product documentation would be + appreciated but is not required. + 2. Altered source versions must be plainly marked as such, and must not be + misrepresented as being the original software. + 3. This notice may not be removed or altered from any source distribution. + + Author: Ladislav Kavan, kavanl@cs.tcd.ie + + Changes for Blender: + - renaming, style changes and optimizations + - added support for scaling +*/ + +void Mat4ToDQuat(float basemat[][4], float mat[][4], DualQuat *dq) +{ + float *t, *q, dscale[3], scale[3], basequat[4]; + float baseRS[4][4], baseinv[4][4], baseR[4][4], baseRinv[4][4]; + float R[4][4], S[4][4]; + + /* split scaling and rotation, there is probably a faster way to do + this, it's done like this now to correctly get negative scaling */ + Mat4MulMat4(baseRS, basemat, mat); + Mat4ToSize(baseRS, scale); + + VecCopyf(dscale, scale); + dscale[0] -= 1.0f; dscale[1] -= 1.0f; dscale[2] -= 1.0f; + + if((Det4x4(mat) < 0.0f) || VecLength(dscale) > 1e-4) { + /* extract R and S */ + Mat4ToQuat(baseRS, basequat); + QuatToMat4(basequat, baseR); + VecCopyf(baseR[3], baseRS[3]); + + Mat4Invert(baseinv, basemat); + Mat4MulMat4(R, baseinv, baseR); + + Mat4Invert(baseRinv, baseR); + Mat4MulMat4(S, baseRS, baseRinv); + + /* set scaling part */ + Mat4MulSerie(dq->scale, basemat, S, baseinv, 0, 0, 0, 0, 0); + dq->scale_weight= 1.0f; + } + else { + /* matrix does not contain scaling */ + Mat4CpyMat4(R, mat); + dq->scale_weight= 0.0f; + } + + /* non-dual part */ + Mat4ToQuat(R, dq->quat); + + /* dual part */ + t= R[3]; + q= dq->quat; + dq->trans[0]= -0.5f*( t[0]*q[1] + t[1]*q[2] + t[2]*q[3]); + dq->trans[1]= 0.5f*( t[0]*q[0] + t[1]*q[3] - t[2]*q[2]); + dq->trans[2]= 0.5f*(-t[0]*q[3] + t[1]*q[0] + t[2]*q[1]); + dq->trans[3]= 0.5f*( t[0]*q[2] - t[1]*q[1] + t[2]*q[0]); +} + +void DQuatToMat4(DualQuat *dq, float mat[][4]) +{ + float len, *t, q0[4]; + + /* regular quaternion */ + QuatCopy(q0, dq->quat); + + /* normalize */ + len= sqrt(QuatDot(q0, q0)); + if(len != 0.0f) + QuatMulf(q0, 1.0f/len); + + /* rotation */ + QuatToMat4(q0, mat); + + /* translation */ + t= dq->trans; + mat[3][0]= 2.0*(-t[0]*q0[1] + t[1]*q0[0] - t[2]*q0[3] + t[3]*q0[2]); + mat[3][1]= 2.0*(-t[0]*q0[2] + t[1]*q0[3] + t[2]*q0[0] - t[3]*q0[1]); + mat[3][2]= 2.0*(-t[0]*q0[3] - t[1]*q0[2] + t[2]*q0[1] + t[3]*q0[0]); + + /* note: this does not handle scaling */ +} + +void DQuatAddWeighted(DualQuat *dqsum, DualQuat *dq, float weight) +{ + /* make sure we interpolate quats in the right direction */ + if (QuatDot(dq->quat, dqsum->quat) < 0) + weight = -weight; + + /* interpolate rotation and translation */ + dqsum->quat[0] += weight*dq->quat[0]; + dqsum->quat[1] += weight*dq->quat[1]; + dqsum->quat[2] += weight*dq->quat[2]; + dqsum->quat[3] += weight*dq->quat[3]; + + dqsum->trans[0] += weight*dq->trans[0]; + dqsum->trans[1] += weight*dq->trans[1]; + dqsum->trans[2] += weight*dq->trans[2]; + dqsum->trans[3] += weight*dq->trans[3]; + + /* interpolate scale - but only if needed */ + if (dq->scale_weight) { + float wmat[4][4]; + + Mat4CpyMat4(wmat, dq->scale); + Mat4MulFloat((float*)wmat, weight); + Mat4AddMat4(dqsum->scale, dqsum->scale, wmat); + dqsum->scale_weight += weight; + } +} + +void DQuatNormalize(DualQuat *dq, float totweight, float factor) +{ + float scale= factor/totweight; + + QuatMulf(dq->quat, scale); + QuatMulf(dq->trans, scale); + + if(dq->scale_weight) { + float addweight= totweight - dq->scale_weight; + + if(addweight) { + dq->scale[0][0] += addweight; + dq->scale[1][1] += addweight; + dq->scale[2][2] += addweight; + dq->scale[3][3] += addweight; + } + + Mat4MulFloat((float*)dq->scale, scale); + dq->scale_weight= 1.0f; + } +} + +void DQuatMulVecfl(DualQuat *dq, float *co, float mat[][3]) +{ + float M[3][3], t[3], scalemat[3][3], len2; + float w= dq->quat[0], x= dq->quat[1], y= dq->quat[2], z= dq->quat[3]; + float t0= dq->trans[0], t1= dq->trans[1], t2= dq->trans[2], t3= dq->trans[3]; + + /* rotation matrix */ + M[0][0]= w*w + x*x - y*y - z*z; + M[1][0]= 2*(x*y - w*z); + M[2][0]= 2*(x*z + w*y); + + M[0][1]= 2*(x*y + w*z); + M[1][1]= w*w + y*y - x*x - z*z; + M[2][1]= 2*(y*z - w*x); + + M[0][2]= 2*(x*z - w*y); + M[1][2]= 2*(y*z + w*x); + M[2][2]= w*w + z*z - x*x - y*y; + + len2= QuatDot(dq->quat, dq->quat); + if(len2 > 0.0f) + len2= 1.0f/len2; + + /* translation */ + t[0]= 2*(-t0*x + w*t1 - t2*z + y*t3); + t[1]= 2*(-t0*y + t1*z - x*t3 + w*t2); + t[2]= 2*(-t0*z + x*t2 + w*t3 - t1*y); + + /* apply scaling */ + if(dq->scale_weight) + Mat4MulVecfl(dq->scale, co); + + /* apply rotation and translation */ + Mat3MulVecfl(M, co); + co[0]= (co[0] + t[0])*len2; + co[1]= (co[1] + t[1])*len2; + co[2]= (co[2] + t[2])*len2; + + /* compute crazyspace correction mat */ + if(mat) { + if(dq->scale_weight) { + Mat3CpyMat4(scalemat, dq->scale); + Mat3MulMat3(mat, M, scalemat); + } + else + Mat3CpyMat3(mat, M); + Mat3MulFloat((float*)mat, len2); + } +} + +void DQuatCpyDQuat(DualQuat *dq1, DualQuat *dq2) +{ + memcpy(dq1, dq2, sizeof(DualQuat)); +} + +/* **************** VIEW / PROJECTION ******************************** */ + + +void i_ortho( + float left, float right, + float bottom, float top, + float nearClip, float farClip, + float matrix[][4] +){ + float Xdelta, Ydelta, Zdelta; + + Xdelta = right - left; + Ydelta = top - bottom; + Zdelta = farClip - nearClip; + if (Xdelta == 0.0 || Ydelta == 0.0 || Zdelta == 0.0) { + return; + } + Mat4One(matrix); + matrix[0][0] = 2.0f/Xdelta; + matrix[3][0] = -(right + left)/Xdelta; + matrix[1][1] = 2.0f/Ydelta; + matrix[3][1] = -(top + bottom)/Ydelta; + matrix[2][2] = -2.0f/Zdelta; /* note: negate Z */ + matrix[3][2] = -(farClip + nearClip)/Zdelta; +} + +void i_window( + float left, float right, + float bottom, float top, + float nearClip, float farClip, + float mat[][4] +){ + float Xdelta, Ydelta, Zdelta; + + Xdelta = right - left; + Ydelta = top - bottom; + Zdelta = farClip - nearClip; + + if (Xdelta == 0.0 || Ydelta == 0.0 || Zdelta == 0.0) { + return; + } + mat[0][0] = nearClip * 2.0f/Xdelta; + mat[1][1] = nearClip * 2.0f/Ydelta; + mat[2][0] = (right + left)/Xdelta; /* note: negate Z */ + mat[2][1] = (top + bottom)/Ydelta; + mat[2][2] = -(farClip + nearClip)/Zdelta; + mat[2][3] = -1.0f; + mat[3][2] = (-2.0f * nearClip * farClip)/Zdelta; + mat[0][1] = mat[0][2] = mat[0][3] = + mat[1][0] = mat[1][2] = mat[1][3] = + mat[3][0] = mat[3][1] = mat[3][3] = 0.0; + +} + +void i_translate(float Tx, float Ty, float Tz, float mat[][4]) +{ + mat[3][0] += (Tx*mat[0][0] + Ty*mat[1][0] + Tz*mat[2][0]); + mat[3][1] += (Tx*mat[0][1] + Ty*mat[1][1] + Tz*mat[2][1]); + mat[3][2] += (Tx*mat[0][2] + Ty*mat[1][2] + Tz*mat[2][2]); +} + +void i_multmatrix( float icand[][4], float Vm[][4]) +{ + int row, col; + float temp[4][4]; + + for(row=0 ; row<4 ; row++) + for(col=0 ; col<4 ; col++) + temp[row][col] = icand[row][0] * Vm[0][col] + + icand[row][1] * Vm[1][col] + + icand[row][2] * Vm[2][col] + + icand[row][3] * Vm[3][col]; + Mat4CpyMat4(Vm, temp); +} + +void i_rotate(float angle, char axis, float mat[][4]) +{ + int col; + float temp[4]; + float cosine, sine; + + for(col=0; col<4 ; col++) /* init temp to zero matrix */ + temp[col] = 0; + + angle = (float)(angle*(3.1415926535/180.0)); + cosine = (float)cos(angle); + sine = (float)sin(angle); + switch(axis){ + case 'x': + case 'X': + for(col=0 ; col<4 ; col++) + temp[col] = cosine*mat[1][col] + sine*mat[2][col]; + for(col=0 ; col<4 ; col++) { + mat[2][col] = - sine*mat[1][col] + cosine*mat[2][col]; + mat[1][col] = temp[col]; + } + break; + + case 'y': + case 'Y': + for(col=0 ; col<4 ; col++) + temp[col] = cosine*mat[0][col] - sine*mat[2][col]; + for(col=0 ; col<4 ; col++) { + mat[2][col] = sine*mat[0][col] + cosine*mat[2][col]; + mat[0][col] = temp[col]; + } + break; + + case 'z': + case 'Z': + for(col=0 ; col<4 ; col++) + temp[col] = cosine*mat[0][col] + sine*mat[1][col]; + for(col=0 ; col<4 ; col++) { + mat[1][col] = - sine*mat[0][col] + cosine*mat[1][col]; + mat[0][col] = temp[col]; + } + break; + } +} + +void i_polarview(float dist, float azimuth, float incidence, float twist, float Vm[][4]) +{ + + Mat4One(Vm); + + i_translate(0.0, 0.0, -dist, Vm); + i_rotate(-twist,'z', Vm); + i_rotate(-incidence,'x', Vm); + i_rotate(-azimuth,'z', Vm); +} + +void i_lookat(float vx, float vy, float vz, float px, float py, float pz, float twist, float mat[][4]) +{ + float sine, cosine, hyp, hyp1, dx, dy, dz; + float mat1[4][4]; + + Mat4One(mat); + Mat4One(mat1); + + i_rotate(-twist,'z', mat); + + dx = px - vx; + dy = py - vy; + dz = pz - vz; + hyp = dx * dx + dz * dz; /* hyp squared */ + hyp1 = (float)sqrt(dy*dy + hyp); + hyp = (float)sqrt(hyp); /* the real hyp */ + + if (hyp1 != 0.0) { /* rotate X */ + sine = -dy / hyp1; + cosine = hyp /hyp1; + } else { + sine = 0; + cosine = 1.0f; + } + mat1[1][1] = cosine; + mat1[1][2] = sine; + mat1[2][1] = -sine; + mat1[2][2] = cosine; + + i_multmatrix(mat1, mat); + + mat1[1][1] = mat1[2][2] = 1.0f; /* be careful here to reinit */ + mat1[1][2] = mat1[2][1] = 0.0; /* those modified by the last */ + + /* paragraph */ + if (hyp != 0.0f) { /* rotate Y */ + sine = dx / hyp; + cosine = -dz / hyp; + } else { + sine = 0; + cosine = 1.0f; + } + mat1[0][0] = cosine; + mat1[0][2] = -sine; + mat1[2][0] = sine; + mat1[2][2] = cosine; + + i_multmatrix(mat1, mat); + i_translate(-vx,-vy,-vz, mat); /* translate viewpoint to origin */ +} + + + + + +/* ************************************************ */ + +void Mat3Ortho(float mat[][3]) +{ + Normalize(mat[0]); + Normalize(mat[1]); + Normalize(mat[2]); +} + +void Mat4Ortho(float mat[][4]) +{ + float len; + + len= Normalize(mat[0]); + if(len!=0.0) mat[0][3]/= len; + len= Normalize(mat[1]); + if(len!=0.0) mat[1][3]/= len; + len= Normalize(mat[2]); + if(len!=0.0) mat[2][3]/= len; +} + +void VecCopyf(float *v1, float *v2) +{ + v1[0]= v2[0]; + v1[1]= v2[1]; + v1[2]= v2[2]; +} + +int VecLen( int *v1, int *v2) +{ + float x,y,z; + + x=(float)(v1[0]-v2[0]); + y=(float)(v1[1]-v2[1]); + z=(float)(v1[2]-v2[2]); + return (int)floor(sqrt(x*x+y*y+z*z)); +} + +float VecLenf( float *v1, float *v2) +{ + float x,y,z; + + x=v1[0]-v2[0]; + y=v1[1]-v2[1]; + z=v1[2]-v2[2]; + return (float)sqrt(x*x+y*y+z*z); +} + +float VecLength(float *v) +{ + return (float) sqrt(v[0]*v[0] + v[1]*v[1] + v[2]*v[2]); +} + +void VecAddf(float *v, float *v1, float *v2) +{ + v[0]= v1[0]+ v2[0]; + v[1]= v1[1]+ v2[1]; + v[2]= v1[2]+ v2[2]; +} + +void VecSubf(float *v, float *v1, float *v2) +{ + v[0]= v1[0]- v2[0]; + v[1]= v1[1]- v2[1]; + v[2]= v1[2]- v2[2]; +} + +void VecLerpf(float *target, float *a, float *b, float t) +{ + float s = 1.0f-t; + + target[0]= s*a[0] + t*b[0]; + target[1]= s*a[1] + t*b[1]; + target[2]= s*a[2] + t*b[2]; +} + +void VecMidf(float *v, float *v1, float *v2) +{ + v[0]= 0.5f*(v1[0]+ v2[0]); + v[1]= 0.5f*(v1[1]+ v2[1]); + v[2]= 0.5f*(v1[2]+ v2[2]); +} + +void VecMulf(float *v1, float f) +{ + + v1[0]*= f; + v1[1]*= f; + v1[2]*= f; +} + +void VecOrthoBasisf(float *v, float *v1, float *v2) +{ + if (v[0] == 0.0f && v[1] == 0.0f) + { + // degenerate case + v1[0] = 0.0f; v1[1] = 1.0f; v1[2] = 0.0f; + if (v[2] > 0.0f) { + v2[0] = 1.0f; v2[1] = v2[2] = 0.0f; + } + else { + v2[0] = -1.0f; v2[1] = v2[2] = 0.0f; + } + } + else + { + float f = 1.0f/sqrt(v[0]*v[0] + v[1]*v[1]); + v1[0] = v[1]*f; + v1[1] = -v[0]*f; + v1[2] = 0.0f; + + Crossf(v2, v, v1); + } +} + +int VecLenCompare(float *v1, float *v2, float limit) +{ + float x,y,z; + + x=v1[0]-v2[0]; + y=v1[1]-v2[1]; + z=v1[2]-v2[2]; + + return ((x*x + y*y + z*z) < (limit*limit)); +} + +int VecCompare( float *v1, float *v2, float limit) +{ + if( fabs(v1[0]-v2[0])<limit ) + if( fabs(v1[1]-v2[1])<limit ) + if( fabs(v1[2]-v2[2])<limit ) return 1; + return 0; +} + +int VecEqual(float *v1, float *v2) +{ + return ((v1[0]==v2[0]) && (v1[1]==v2[1]) && (v1[2]==v2[2])); +} + +void CalcNormShort( short *v1, short *v2, short *v3, float *n) /* is also cross product */ +{ + float n1[3],n2[3]; + + n1[0]= (float)(v1[0]-v2[0]); + n2[0]= (float)(v2[0]-v3[0]); + n1[1]= (float)(v1[1]-v2[1]); + n2[1]= (float)(v2[1]-v3[1]); + n1[2]= (float)(v1[2]-v2[2]); + n2[2]= (float)(v2[2]-v3[2]); + n[0]= n1[1]*n2[2]-n1[2]*n2[1]; + n[1]= n1[2]*n2[0]-n1[0]*n2[2]; + n[2]= n1[0]*n2[1]-n1[1]*n2[0]; + Normalize(n); +} + +void CalcNormLong( int* v1, int*v2, int*v3, float *n) +{ + float n1[3],n2[3]; + + n1[0]= (float)(v1[0]-v2[0]); + n2[0]= (float)(v2[0]-v3[0]); + n1[1]= (float)(v1[1]-v2[1]); + n2[1]= (float)(v2[1]-v3[1]); + n1[2]= (float)(v1[2]-v2[2]); + n2[2]= (float)(v2[2]-v3[2]); + n[0]= n1[1]*n2[2]-n1[2]*n2[1]; + n[1]= n1[2]*n2[0]-n1[0]*n2[2]; + n[2]= n1[0]*n2[1]-n1[1]*n2[0]; + Normalize(n); +} + +float CalcNormFloat( float *v1, float *v2, float *v3, float *n) +{ + float n1[3],n2[3]; + + n1[0]= v1[0]-v2[0]; + n2[0]= v2[0]-v3[0]; + n1[1]= v1[1]-v2[1]; + n2[1]= v2[1]-v3[1]; + n1[2]= v1[2]-v2[2]; + n2[2]= v2[2]-v3[2]; + n[0]= n1[1]*n2[2]-n1[2]*n2[1]; + n[1]= n1[2]*n2[0]-n1[0]*n2[2]; + n[2]= n1[0]*n2[1]-n1[1]*n2[0]; + return Normalize(n); +} + +float CalcNormFloat4( float *v1, float *v2, float *v3, float *v4, float *n) +{ + /* real cross! */ + float n1[3],n2[3]; + + n1[0]= v1[0]-v3[0]; + n1[1]= v1[1]-v3[1]; + n1[2]= v1[2]-v3[2]; + + n2[0]= v2[0]-v4[0]; + n2[1]= v2[1]-v4[1]; + n2[2]= v2[2]-v4[2]; + + n[0]= n1[1]*n2[2]-n1[2]*n2[1]; + n[1]= n1[2]*n2[0]-n1[0]*n2[2]; + n[2]= n1[0]*n2[1]-n1[1]*n2[0]; + + return Normalize(n); +} + + +void CalcCent3f(float *cent, float *v1, float *v2, float *v3) +{ + + cent[0]= 0.33333f*(v1[0]+v2[0]+v3[0]); + cent[1]= 0.33333f*(v1[1]+v2[1]+v3[1]); + cent[2]= 0.33333f*(v1[2]+v2[2]+v3[2]); +} + +void CalcCent4f(float *cent, float *v1, float *v2, float *v3, float *v4) +{ + + cent[0]= 0.25f*(v1[0]+v2[0]+v3[0]+v4[0]); + cent[1]= 0.25f*(v1[1]+v2[1]+v3[1]+v4[1]); + cent[2]= 0.25f*(v1[2]+v2[2]+v3[2]+v4[2]); +} + +float Sqrt3f(float f) +{ + if(f==0.0) return 0; + if(f<0) return (float)(-exp(log(-f)/3)); + else return (float)(exp(log(f)/3)); +} + +double Sqrt3d(double d) +{ + if(d==0.0) return 0; + if(d<0) return -exp(log(-d)/3); + else return exp(log(d)/3); +} + +/* distance v1 to line v2-v3 */ +/* using Hesse formula, NO LINE PIECE! */ +float DistVL2Dfl( float *v1, float *v2, float *v3) { + float a[2],deler; + + a[0]= v2[1]-v3[1]; + a[1]= v3[0]-v2[0]; + deler= (float)sqrt(a[0]*a[0]+a[1]*a[1]); + if(deler== 0.0f) return 0; + + return (float)(fabs((v1[0]-v2[0])*a[0]+(v1[1]-v2[1])*a[1])/deler); + +} + +/* distance v1 to line-piece v2-v3 */ +float PdistVL2Dfl( float *v1, float *v2, float *v3) +{ + float labda, rc[2], pt[2], len; + + rc[0]= v3[0]-v2[0]; + rc[1]= v3[1]-v2[1]; + len= rc[0]*rc[0]+ rc[1]*rc[1]; + if(len==0.0) { + rc[0]= v1[0]-v2[0]; + rc[1]= v1[1]-v2[1]; + return (float)(sqrt(rc[0]*rc[0]+ rc[1]*rc[1])); + } + + labda= ( rc[0]*(v1[0]-v2[0]) + rc[1]*(v1[1]-v2[1]) )/len; + if(labda<=0.0) { + pt[0]= v2[0]; + pt[1]= v2[1]; + } + else if(labda>=1.0) { + pt[0]= v3[0]; + pt[1]= v3[1]; + } + else { + pt[0]= labda*rc[0]+v2[0]; + pt[1]= labda*rc[1]+v2[1]; + } + + rc[0]= pt[0]-v1[0]; + rc[1]= pt[1]-v1[1]; + return (float)sqrt(rc[0]*rc[0]+ rc[1]*rc[1]); +} + +float AreaF2Dfl( float *v1, float *v2, float *v3) +{ + return (float)(0.5*fabs( (v1[0]-v2[0])*(v2[1]-v3[1]) + (v1[1]-v2[1])*(v3[0]-v2[0]) )); +} + + +float AreaQ3Dfl( float *v1, float *v2, float *v3, float *v4) /* only convex Quadrilaterals */ +{ + float len, vec1[3], vec2[3], n[3]; + + VecSubf(vec1, v2, v1); + VecSubf(vec2, v4, v1); + Crossf(n, vec1, vec2); + len= Normalize(n); + + VecSubf(vec1, v4, v3); + VecSubf(vec2, v2, v3); + Crossf(n, vec1, vec2); + len+= Normalize(n); + + return (len/2.0f); +} + +float AreaT3Dfl( float *v1, float *v2, float *v3) /* Triangles */ +{ + float len, vec1[3], vec2[3], n[3]; + + VecSubf(vec1, v3, v2); + VecSubf(vec2, v1, v2); + Crossf(n, vec1, vec2); + len= Normalize(n); + + return (len/2.0f); +} + +#define MAX2(x,y) ( (x)>(y) ? (x) : (y) ) +#define MAX3(x,y,z) MAX2( MAX2((x),(y)) , (z) ) + + +float AreaPoly3Dfl(int nr, float *verts, float *normal) +{ + float x, y, z, area, max; + float *cur, *prev; + int a, px=0, py=1; + + /* first: find dominant axis: 0==X, 1==Y, 2==Z */ + x= (float)fabs(normal[0]); + y= (float)fabs(normal[1]); + z= (float)fabs(normal[2]); + max = MAX3(x, y, z); + if(max==y) py=2; + else if(max==x) { + px=1; + py= 2; + } + + /* The Trapezium Area Rule */ + prev= verts+3*(nr-1); + cur= verts; + area= 0; + for(a=0; a<nr; a++) { + area+= (cur[px]-prev[px])*(cur[py]+prev[py]); + prev= cur; + cur+=3; + } + + return (float)fabs(0.5*area/max); +} + +/* intersect Line-Line, shorts */ +short IsectLL2Ds(short *v1, short *v2, short *v3, short *v4) +{ + /* return: + -1: colliniar + 0: no intersection of segments + 1: exact intersection of segments + 2: cross-intersection of segments + */ + float div, labda, mu; + + div= (v2[0]-v1[0])*(v4[1]-v3[1])-(v2[1]-v1[1])*(v4[0]-v3[0]); + if(div==0.0) return -1; + + labda= ((float)(v1[1]-v3[1])*(v4[0]-v3[0])-(v1[0]-v3[0])*(v4[1]-v3[1]))/div; + + mu= ((float)(v1[1]-v3[1])*(v2[0]-v1[0])-(v1[0]-v3[0])*(v2[1]-v1[1]))/div; + + if(labda>=0.0 && labda<=1.0 && mu>=0.0 && mu<=1.0) { + if(labda==0.0 || labda==1.0 || mu==0.0 || mu==1.0) return 1; + return 2; + } + return 0; +} + +/* intersect Line-Line, floats */ +short IsectLL2Df(float *v1, float *v2, float *v3, float *v4) +{ + /* return: + -1: colliniar +0: no intersection of segments +1: exact intersection of segments +2: cross-intersection of segments + */ + float div, labda, mu; + + div= (v2[0]-v1[0])*(v4[1]-v3[1])-(v2[1]-v1[1])*(v4[0]-v3[0]); + if(div==0.0) return -1; + + labda= ((float)(v1[1]-v3[1])*(v4[0]-v3[0])-(v1[0]-v3[0])*(v4[1]-v3[1]))/div; + + mu= ((float)(v1[1]-v3[1])*(v2[0]-v1[0])-(v1[0]-v3[0])*(v2[1]-v1[1]))/div; + + if(labda>=0.0 && labda<=1.0 && mu>=0.0 && mu<=1.0) { + if(labda==0.0 || labda==1.0 || mu==0.0 || mu==1.0) return 1; + return 2; + } + return 0; +} + +void MinMax3(float *min, float *max, float *vec) +{ + if(min[0]>vec[0]) min[0]= vec[0]; + if(min[1]>vec[1]) min[1]= vec[1]; + if(min[2]>vec[2]) min[2]= vec[2]; + + if(max[0]<vec[0]) max[0]= vec[0]; + if(max[1]<vec[1]) max[1]= vec[1]; + if(max[2]<vec[2]) max[2]= vec[2]; +} + +static float TriSignedArea(float *v1, float *v2, float *v3, int i, int j) +{ + return 0.5f*((v1[i]-v2[i])*(v2[j]-v3[j]) + (v1[j]-v2[j])*(v3[i]-v2[i])); +} + +static int BarycentricWeights(float *v1, float *v2, float *v3, float *co, float *n, float *w) +{ + float xn, yn, zn, a1, a2, a3, asum; + short i, j; + + /* find best projection of face XY, XZ or YZ: barycentric weights of + the 2d projected coords are the same and faster to compute */ + xn= fabs(n[0]); + yn= fabs(n[1]); + zn= fabs(n[2]); + if(zn>=xn && zn>=yn) {i= 0; j= 1;} + else if(yn>=xn && yn>=zn) {i= 0; j= 2;} + else {i= 1; j= 2;} + + a1= TriSignedArea(v2, v3, co, i, j); + a2= TriSignedArea(v3, v1, co, i, j); + a3= TriSignedArea(v1, v2, co, i, j); + + asum= a1 + a2 + a3; + + if (fabs(asum) < FLT_EPSILON) { + /* zero area triangle */ + w[0]= w[1]= w[2]= 1.0f/3.0f; + return 1; + } + + asum= 1.0f/asum; + w[0]= a1*asum; + w[1]= a2*asum; + w[2]= a3*asum; + + return 0; +} + +void InterpWeightsQ3Dfl(float *v1, float *v2, float *v3, float *v4, float *co, float *w) +{ + float w2[3]; + + w[0]= w[1]= w[2]= w[3]= 0.0f; + + /* first check for exact match */ + if(VecEqual(co, v1)) + w[0]= 1.0f; + else if(VecEqual(co, v2)) + w[1]= 1.0f; + else if(VecEqual(co, v3)) + w[2]= 1.0f; + else if(v4 && VecEqual(co, v4)) + w[3]= 1.0f; + else { + /* otherwise compute barycentric interpolation weights */ + float n1[3], n2[3], n[3]; + int degenerate; + + VecSubf(n1, v1, v3); + if (v4) { + VecSubf(n2, v2, v4); + } + else { + VecSubf(n2, v2, v3); + } + Crossf(n, n1, n2); + + /* OpenGL seems to split this way, so we do too */ + if (v4) { + degenerate= BarycentricWeights(v1, v2, v4, co, n, w); + SWAP(float, w[2], w[3]); + + if(degenerate || (w[0] < 0.0f)) { + /* if w[1] is negative, co is on the other side of the v1-v3 edge, + so we interpolate using the other triangle */ + degenerate= BarycentricWeights(v2, v3, v4, co, n, w2); + + if(!degenerate) { + w[0]= 0.0f; + w[1]= w2[0]; + w[2]= w2[1]; + w[3]= w2[2]; + } + } + } + else + BarycentricWeights(v1, v2, v3, co, n, w); + } +} + +/* Mean value weights - smooth interpolation weights for polygons with + * more than 3 vertices */ +static float MeanValueHalfTan(float *v1, float *v2, float *v3) +{ + float d2[3], d3[3], cross[3], area, dot, len; + + VecSubf(d2, v2, v1); + VecSubf(d3, v3, v1); + Crossf(cross, d2, d3); + + area= VecLength(cross); + dot= Inpf(d2, d3); + len= VecLength(d2)*VecLength(d3); + + if(area == 0.0f) + return 0.0f; + else + return (len - dot)/area; +} + +void MeanValueWeights(float v[][3], int n, float *co, float *w) +{ + float totweight, t1, t2, len, *vmid, *vprev, *vnext; + int i; + + totweight= 0.0f; + + for(i=0; i<n; i++) { + vmid= v[i]; + vprev= (i == 0)? v[n-1]: v[i-1]; + vnext= (i == n-1)? v[0]: v[i+1]; + + t1= MeanValueHalfTan(co, vprev, vmid); + t2= MeanValueHalfTan(co, vmid, vnext); + + len= VecLenf(co, vmid); + w[i]= (t1+t2)/len; + totweight += w[i]; + } + + if(totweight != 0.0f) + for(i=0; i<n; i++) + w[i] /= totweight; +} + + +/* ************ EULER *************** */ + +void EulToMat3( float *eul, float mat[][3]) +{ + double ci, cj, ch, si, sj, sh, cc, cs, sc, ss; + + ci = cos(eul[0]); + cj = cos(eul[1]); + ch = cos(eul[2]); + si = sin(eul[0]); + sj = sin(eul[1]); + sh = sin(eul[2]); + cc = ci*ch; + cs = ci*sh; + sc = si*ch; + ss = si*sh; + + mat[0][0] = (float)(cj*ch); + mat[1][0] = (float)(sj*sc-cs); + mat[2][0] = (float)(sj*cc+ss); + mat[0][1] = (float)(cj*sh); + mat[1][1] = (float)(sj*ss+cc); + mat[2][1] = (float)(sj*cs-sc); + mat[0][2] = (float)-sj; + mat[1][2] = (float)(cj*si); + mat[2][2] = (float)(cj*ci); + +} + +void EulToMat4( float *eul,float mat[][4]) +{ + double ci, cj, ch, si, sj, sh, cc, cs, sc, ss; + + ci = cos(eul[0]); + cj = cos(eul[1]); + ch = cos(eul[2]); + si = sin(eul[0]); + sj = sin(eul[1]); + sh = sin(eul[2]); + cc = ci*ch; + cs = ci*sh; + sc = si*ch; + ss = si*sh; + + mat[0][0] = (float)(cj*ch); + mat[1][0] = (float)(sj*sc-cs); + mat[2][0] = (float)(sj*cc+ss); + mat[0][1] = (float)(cj*sh); + mat[1][1] = (float)(sj*ss+cc); + mat[2][1] = (float)(sj*cs-sc); + mat[0][2] = (float)-sj; + mat[1][2] = (float)(cj*si); + mat[2][2] = (float)(cj*ci); + + + mat[3][0]= mat[3][1]= mat[3][2]= mat[0][3]= mat[1][3]= mat[2][3]= 0.0f; + mat[3][3]= 1.0f; +} + +/* returns two euler calculation methods, so we can pick the best */ +static void mat3_to_eul2(float tmat[][3], float *eul1, float *eul2) +{ + float cy, quat[4], mat[3][3]; + + Mat3ToQuat(tmat, quat); + QuatToMat3(quat, mat); + Mat3CpyMat3(mat, tmat); + Mat3Ortho(mat); + + cy = (float)sqrt(mat[0][0]*mat[0][0] + mat[0][1]*mat[0][1]); + + if (cy > 16.0*FLT_EPSILON) { + + eul1[0] = (float)atan2(mat[1][2], mat[2][2]); + eul1[1] = (float)atan2(-mat[0][2], cy); + eul1[2] = (float)atan2(mat[0][1], mat[0][0]); + + eul2[0] = (float)atan2(-mat[1][2], -mat[2][2]); + eul2[1] = (float)atan2(-mat[0][2], -cy); + eul2[2] = (float)atan2(-mat[0][1], -mat[0][0]); + + } else { + eul1[0] = (float)atan2(-mat[2][1], mat[1][1]); + eul1[1] = (float)atan2(-mat[0][2], cy); + eul1[2] = 0.0f; + + VecCopyf(eul2, eul1); + } +} + +void Mat3ToEul(float tmat[][3], float *eul) +{ + float eul1[3], eul2[3]; + + mat3_to_eul2(tmat, eul1, eul2); + + /* return best, which is just the one with lowest values it in */ + if( fabs(eul1[0])+fabs(eul1[1])+fabs(eul1[2]) > fabs(eul2[0])+fabs(eul2[1])+fabs(eul2[2])) { + VecCopyf(eul, eul2); + } + else { + VecCopyf(eul, eul1); + } +} + +void Mat4ToEul(float tmat[][4], float *eul) +{ + float tempMat[3][3]; + + Mat3CpyMat4 (tempMat, tmat); + Mat3Ortho(tempMat); + Mat3ToEul(tempMat, eul); +} + +void QuatToEul( float *quat, float *eul) +{ + float mat[3][3]; + + QuatToMat3(quat, mat); + Mat3ToEul(mat, eul); +} + + +void EulToQuat( float *eul, float *quat) +{ + float ti, tj, th, ci, cj, ch, si, sj, sh, cc, cs, sc, ss; + + ti = eul[0]*0.5f; tj = eul[1]*0.5f; th = eul[2]*0.5f; + ci = (float)cos(ti); cj = (float)cos(tj); ch = (float)cos(th); + si = (float)sin(ti); sj = (float)sin(tj); sh = (float)sin(th); + cc = ci*ch; cs = ci*sh; sc = si*ch; ss = si*sh; + + quat[0] = cj*cc + sj*ss; + quat[1] = cj*sc - sj*cs; + quat[2] = cj*ss + sj*cc; + quat[3] = cj*cs - sj*sc; +} + +void VecRotToMat3( float *vec, float phi, float mat[][3]) +{ + /* rotation of phi radials around vec */ + float vx, vx2, vy, vy2, vz, vz2, co, si; + + vx= vec[0]; + vy= vec[1]; + vz= vec[2]; + vx2= vx*vx; + vy2= vy*vy; + vz2= vz*vz; + co= (float)cos(phi); + si= (float)sin(phi); + + mat[0][0]= vx2+co*(1.0f-vx2); + mat[0][1]= vx*vy*(1.0f-co)+vz*si; + mat[0][2]= vz*vx*(1.0f-co)-vy*si; + mat[1][0]= vx*vy*(1.0f-co)-vz*si; + mat[1][1]= vy2+co*(1.0f-vy2); + mat[1][2]= vy*vz*(1.0f-co)+vx*si; + mat[2][0]= vz*vx*(1.0f-co)+vy*si; + mat[2][1]= vy*vz*(1.0f-co)-vx*si; + mat[2][2]= vz2+co*(1.0f-vz2); + +} + +void VecRotToMat4( float *vec, float phi, float mat[][4]) +{ + float tmat[3][3]; + + VecRotToMat3(vec, phi, tmat); + Mat4One(mat); + Mat4CpyMat3(mat, tmat); +} + +void VecRotToQuat( float *vec, float phi, float *quat) +{ + /* rotation of phi radials around vec */ + float si; + + quat[1]= vec[0]; + quat[2]= vec[1]; + quat[3]= vec[2]; + + if( Normalize(quat+1) == 0.0) { + QuatOne(quat); + } + else { + quat[0]= (float)cos( phi/2.0 ); + si= (float)sin( phi/2.0 ); + quat[1] *= si; + quat[2] *= si; + quat[3] *= si; + } +} + +/* Return the angle in degrees between vecs 1-2 and 2-3 in degrees + If v1 is a shoulder, v2 is the elbow and v3 is the hand, + this would return the angle at the elbow */ +float VecAngle3(float *v1, float *v2, float *v3) +{ + float vec1[3], vec2[3]; + + VecSubf(vec1, v2, v1); + VecSubf(vec2, v2, v3); + Normalize(vec1); + Normalize(vec2); + + return NormalizedVecAngle2(vec1, vec2) * 180.0/M_PI; +} + +/* Return the shortest angle in degrees between the 2 vectors */ +float VecAngle2(float *v1, float *v2) +{ + float vec1[3], vec2[3]; + + VecCopyf(vec1, v1); + VecCopyf(vec2, v2); + Normalize(vec1); + Normalize(vec2); + + return NormalizedVecAngle2(vec1, vec2)* 180.0/M_PI; +} + +float NormalizedVecAngle2(float *v1, float *v2) +{ + /* this is the same as acos(Inpf(v1, v2)), but more accurate */ + if (Inpf(v1, v2) < 0.0f) { + float vec[3]; + + vec[0]= -v2[0]; + vec[1]= -v2[1]; + vec[2]= -v2[2]; + + return (float)M_PI - 2.0f*saasin(VecLenf(vec, v1)/2.0f); + } + else + return 2.0f*saasin(VecLenf(v2, v1)/2.0); +} + +void euler_rot(float *beul, float ang, char axis) +{ + float eul[3], mat1[3][3], mat2[3][3], totmat[3][3]; + + eul[0]= eul[1]= eul[2]= 0.0; + if(axis=='x') eul[0]= ang; + else if(axis=='y') eul[1]= ang; + else eul[2]= ang; + + EulToMat3(eul, mat1); + EulToMat3(beul, mat2); + + Mat3MulMat3(totmat, mat2, mat1); + + Mat3ToEul(totmat, beul); + +} + +/* exported to transform.c */ +void compatible_eul(float *eul, float *oldrot) +{ + float dx, dy, dz; + + /* correct differences of about 360 degrees first */ + + dx= eul[0] - oldrot[0]; + dy= eul[1] - oldrot[1]; + dz= eul[2] - oldrot[2]; + + while( fabs(dx) > 5.1) { + if(dx > 0.0) eul[0] -= 2.0*M_PI; else eul[0]+= 2.0*M_PI; + dx= eul[0] - oldrot[0]; + } + while( fabs(dy) > 5.1) { + if(dy > 0.0) eul[1] -= 2.0*M_PI; else eul[1]+= 2.0*M_PI; + dy= eul[1] - oldrot[1]; + } + while( fabs(dz) > 5.1 ) { + if(dz > 0.0) eul[2] -= 2.0*M_PI; else eul[2]+= 2.0*M_PI; + dz= eul[2] - oldrot[2]; + } + + /* is 1 of the axis rotations larger than 180 degrees and the other small? NO ELSE IF!! */ + if( fabs(dx) > 3.2 && fabs(dy)<1.6 && fabs(dz)<1.6 ) { + if(dx > 0.0) eul[0] -= 2.0*M_PI; else eul[0]+= 2.0*M_PI; + } + if( fabs(dy) > 3.2 && fabs(dz)<1.6 && fabs(dx)<1.6 ) { + if(dy > 0.0) eul[1] -= 2.0*M_PI; else eul[1]+= 2.0*M_PI; + } + if( fabs(dz) > 3.2 && fabs(dx)<1.6 && fabs(dy)<1.6 ) { + if(dz > 0.0) eul[2] -= 2.0*M_PI; else eul[2]+= 2.0*M_PI; + } + + /* the method below was there from ancient days... but why! probably because the code sucks :) + */ +#if 0 + /* calc again */ + dx= eul[0] - oldrot[0]; + dy= eul[1] - oldrot[1]; + dz= eul[2] - oldrot[2]; + + /* special case, tested for x-z */ + + if( (fabs(dx) > 3.1 && fabs(dz) > 1.5 ) || ( fabs(dx) > 1.5 && fabs(dz) > 3.1 ) ) { + if(dx > 0.0) eul[0] -= M_PI; else eul[0]+= M_PI; + if(eul[1] > 0.0) eul[1]= M_PI - eul[1]; else eul[1]= -M_PI - eul[1]; + if(dz > 0.0) eul[2] -= M_PI; else eul[2]+= M_PI; + + } + else if( (fabs(dx) > 3.1 && fabs(dy) > 1.5 ) || ( fabs(dx) > 1.5 && fabs(dy) > 3.1 ) ) { + if(dx > 0.0) eul[0] -= M_PI; else eul[0]+= M_PI; + if(dy > 0.0) eul[1] -= M_PI; else eul[1]+= M_PI; + if(eul[2] > 0.0) eul[2]= M_PI - eul[2]; else eul[2]= -M_PI - eul[2]; + } + else if( (fabs(dy) > 3.1 && fabs(dz) > 1.5 ) || ( fabs(dy) > 1.5 && fabs(dz) > 3.1 ) ) { + if(eul[0] > 0.0) eul[0]= M_PI - eul[0]; else eul[0]= -M_PI - eul[0]; + if(dy > 0.0) eul[1] -= M_PI; else eul[1]+= M_PI; + if(dz > 0.0) eul[2] -= M_PI; else eul[2]+= M_PI; + } +#endif +} + +/* uses 2 methods to retrieve eulers, and picks the closest */ +void Mat3ToCompatibleEul(float mat[][3], float *eul, float *oldrot) +{ + float eul1[3], eul2[3]; + float d1, d2; + + mat3_to_eul2(mat, eul1, eul2); + + compatible_eul(eul1, oldrot); + compatible_eul(eul2, oldrot); + + d1= fabs(eul1[0]-oldrot[0]) + fabs(eul1[1]-oldrot[1]) + fabs(eul1[2]-oldrot[2]); + d2= fabs(eul2[0]-oldrot[0]) + fabs(eul2[1]-oldrot[1]) + fabs(eul2[2]-oldrot[2]); + + /* return best, which is just the one with lowest difference */ + if( d1 > d2) { + VecCopyf(eul, eul2); + } + else { + VecCopyf(eul, eul1); + } + +} + +/* ******************************************** */ + +void SizeToMat3( float *size, float mat[][3]) +{ + mat[0][0]= size[0]; + mat[0][1]= 0.0; + mat[0][2]= 0.0; + mat[1][1]= size[1]; + mat[1][0]= 0.0; + mat[1][2]= 0.0; + mat[2][2]= size[2]; + mat[2][1]= 0.0; + mat[2][0]= 0.0; +} + +void SizeToMat4( float *size, float mat[][4]) +{ + float tmat[3][3]; + + SizeToMat3(size, tmat); + Mat4One(mat); + Mat4CpyMat3(mat, tmat); +} + +void Mat3ToSize( float mat[][3], float *size) +{ + size[0]= VecLength(mat[0]); + size[1]= VecLength(mat[1]); + size[2]= VecLength(mat[2]); +} + +void Mat4ToSize( float mat[][4], float *size) +{ + size[0]= VecLength(mat[0]); + size[1]= VecLength(mat[1]); + size[2]= VecLength(mat[2]); +} + +/* this gets the average scale of a matrix, only use when your scaling + * data that has no idea of scale axis, examples are bone-envelope-radius + * and curve radius */ +float Mat3ToScalef(float mat[][3]) +{ + /* unit length vector */ + float unit_vec[3] = {0.577350269189626, 0.577350269189626, 0.577350269189626}; + Mat3MulVecfl(mat, unit_vec); + return VecLength(unit_vec); +} + +float Mat4ToScalef(float mat[][4]) +{ + float tmat[3][3]; + Mat3CpyMat4(tmat, mat); + return Mat3ToScalef(tmat); +} + + +/* ************* SPECIALS ******************* */ + +void triatoquat( float *v1, float *v2, float *v3, float *quat) +{ + /* imaginary x-axis, y-axis triangle is being rotated */ + float vec[3], q1[4], q2[4], n[3], si, co, angle, mat[3][3], imat[3][3]; + + /* move z-axis to face-normal */ + CalcNormFloat(v1, v2, v3, vec); + + n[0]= vec[1]; + n[1]= -vec[0]; + n[2]= 0.0; + Normalize(n); + + if(n[0]==0.0 && n[1]==0.0) n[0]= 1.0; + + angle= -0.5f*saacos(vec[2]); + co= (float)cos(angle); + si= (float)sin(angle); + q1[0]= co; + q1[1]= n[0]*si; + q1[2]= n[1]*si; + q1[3]= 0.0f; + + /* rotate back line v1-v2 */ + QuatToMat3(q1, mat); + Mat3Inv(imat, mat); + VecSubf(vec, v2, v1); + Mat3MulVecfl(imat, vec); + + /* what angle has this line with x-axis? */ + vec[2]= 0.0; + Normalize(vec); + + angle= (float)(0.5*atan2(vec[1], vec[0])); + co= (float)cos(angle); + si= (float)sin(angle); + q2[0]= co; + q2[1]= 0.0f; + q2[2]= 0.0f; + q2[3]= si; + + QuatMul(quat, q1, q2); +} + +void MinMaxRGB(short c[]) +{ + if(c[0]>255) c[0]=255; + else if(c[0]<0) c[0]=0; + if(c[1]>255) c[1]=255; + else if(c[1]<0) c[1]=0; + if(c[2]>255) c[2]=255; + else if(c[2]<0) c[2]=0; +} + +float Vec2Lenf(float *v1, float *v2) +{ + float x, y; + + x = v1[0]-v2[0]; + y = v1[1]-v2[1]; + return (float)sqrt(x*x+y*y); +} + +void Vec2Mulf(float *v1, float f) +{ + v1[0]*= f; + v1[1]*= f; +} + +void Vec2Addf(float *v, float *v1, float *v2) +{ + v[0]= v1[0]+ v2[0]; + v[1]= v1[1]+ v2[1]; +} + +void Vec2Subf(float *v, float *v1, float *v2) +{ + v[0]= v1[0]- v2[0]; + v[1]= v1[1]- v2[1]; +} + +void Vec2Copyf(float *v1, float *v2) +{ + v1[0]= v2[0]; + v1[1]= v2[1]; +} + +float Inp2f(float *v1, float *v2) +{ + return v1[0]*v2[0]+v1[1]*v2[1]; +} + +float Normalize2(float *n) +{ + float d; + + d= n[0]*n[0]+n[1]*n[1]; + + if(d>1.0e-35F) { + d= (float)sqrt(d); + + n[0]/=d; + n[1]/=d; + } else { + n[0]=n[1]= 0.0; + d= 0.0; + } + return d; +} + +void hsv_to_rgb(float h, float s, float v, float *r, float *g, float *b) +{ + int i; + float f, p, q, t; + + h *= 360.0f; + + if(s==0.0) { + *r = v; + *g = v; + *b = v; + } + else { + if(h==360) h = 0; + + h /= 60; + i = (int)floor(h); + f = h - i; + p = v*(1.0f-s); + q = v*(1.0f-(s*f)); + t = v*(1.0f-(s*(1.0f-f))); + + switch (i) { + case 0 : + *r = v; + *g = t; + *b = p; + break; + case 1 : + *r = q; + *g = v; + *b = p; + break; + case 2 : + *r = p; + *g = v; + *b = t; + break; + case 3 : + *r = p; + *g = q; + *b = v; + break; + case 4 : + *r = t; + *g = p; + *b = v; + break; + case 5 : + *r = v; + *g = p; + *b = q; + break; + } + } +} + +void rgb_to_yuv(float r, float g, float b, float *ly, float *lu, float *lv) +{ + float y, u, v; + y= 0.299*r + 0.587*g + 0.114*b; + u=-0.147*r - 0.289*g + 0.436*b; + v= 0.615*r - 0.515*g - 0.100*b; + + *ly=y; + *lu=u; + *lv=v; +} + +void yuv_to_rgb(float y, float u, float v, float *lr, float *lg, float *lb) +{ + float r, g, b; + r=y+1.140*v; + g=y-0.394*u - 0.581*v; + b=y+2.032*u; + + *lr=r; + *lg=g; + *lb=b; +} + +void rgb_to_ycc(float r, float g, float b, float *ly, float *lcb, float *lcr) +{ + float sr,sg, sb; + float y, cr, cb; + + sr=255.0*r; + sg=255.0*g; + sb=255.0*b; + + + y=(0.257*sr)+(0.504*sg)+(0.098*sb)+16.0; + cb=(-0.148*sr)-(0.291*sg)+(0.439*sb)+128.0; + cr=(0.439*sr)-(0.368*sg)-(0.071*sb)+128.0; + + *ly=y; + *lcb=cb; + *lcr=cr; +} + +void ycc_to_rgb(float y, float cb, float cr, float *lr, float *lg, float *lb) +{ + float r,g,b; + + r=1.164*(y-16)+1.596*(cr-128); + g=1.164*(y-16)-0.813*(cr-128)-0.392*(cb-128); + b=1.164*(y-16)+2.017*(cb-128); + + *lr=r/255.0; + *lg=g/255.0; + *lb=b/255.0; +} + +void hex_to_rgb(char *hexcol, float *r, float *g, float *b) +{ + unsigned int ri, gi, bi; + + if (hexcol[0] == '#') hexcol++; + + if (sscanf(hexcol, "%02x%02x%02x", &ri, &gi, &bi)) { + *r = ri / 255.0; + *g = gi / 255.0; + *b = bi / 255.0; + } +} + +void rgb_to_hsv(float r, float g, float b, float *lh, float *ls, float *lv) +{ + float h, s, v; + float cmax, cmin, cdelta; + float rc, gc, bc; + + cmax = r; + cmin = r; + cmax = (g>cmax ? g:cmax); + cmin = (g<cmin ? g:cmin); + cmax = (b>cmax ? b:cmax); + cmin = (b<cmin ? b:cmin); + + v = cmax; /* value */ + if (cmax!=0.0) + s = (cmax - cmin)/cmax; + else { + s = 0.0; + h = 0.0; + } + if (s == 0.0) + h = -1.0; + else { + cdelta = cmax-cmin; + rc = (cmax-r)/cdelta; + gc = (cmax-g)/cdelta; + bc = (cmax-b)/cdelta; + if (r==cmax) + h = bc-gc; + else + if (g==cmax) + h = 2.0f+rc-bc; + else + h = 4.0f+gc-rc; + h = h*60.0f; + if (h<0.0f) + h += 360.0f; + } + + *ls = s; + *lh = h/360.0f; + if( *lh < 0.0) *lh= 0.0; + *lv = v; +} + + +/* we define a 'cpack' here as a (3 byte color code) number that can be expressed like 0xFFAA66 or so. + for that reason it is sensitive for endianness... with this function it works correctly +*/ + +unsigned int hsv_to_cpack(float h, float s, float v) +{ + short r, g, b; + float rf, gf, bf; + unsigned int col; + + hsv_to_rgb(h, s, v, &rf, &gf, &bf); + + r= (short)(rf*255.0f); + g= (short)(gf*255.0f); + b= (short)(bf*255.0f); + + col= ( r + (g*256) + (b*256*256) ); + return col; +} + + +unsigned int rgb_to_cpack(float r, float g, float b) +{ + int ir, ig, ib; + + ir= (int)floor(255.0*r); + if(ir<0) ir= 0; else if(ir>255) ir= 255; + ig= (int)floor(255.0*g); + if(ig<0) ig= 0; else if(ig>255) ig= 255; + ib= (int)floor(255.0*b); + if(ib<0) ib= 0; else if(ib>255) ib= 255; + + return (ir+ (ig*256) + (ib*256*256)); +} + +void cpack_to_rgb(unsigned int col, float *r, float *g, float *b) +{ + + *r= (float)((col)&0xFF); + *r /= 255.0f; + + *g= (float)(((col)>>8)&0xFF); + *g /= 255.0f; + + *b= (float)(((col)>>16)&0xFF); + *b /= 255.0f; +} + + +/* *************** PROJECTIONS ******************* */ + +void tubemap(float x, float y, float z, float *u, float *v) +{ + float len; + + *v = (z + 1.0) / 2.0; + + len= sqrt(x*x+y*y); + if(len>0) { + *u = (1.0 - (atan2(x/len,y/len) / M_PI)) / 2.0; + } +} + +/* ------------------------------------------------------------------------- */ + +void spheremap(float x, float y, float z, float *u, float *v) +{ + float len; + + len= sqrt(x*x+y*y+z*z); + if(len>0.0) { + + if(x==0.0 && y==0.0) *u= 0.0; /* othwise domain error */ + else *u = (1.0 - atan2(x,y)/M_PI )/2.0; + + z/=len; + *v = 1.0- saacos(z)/M_PI; + } +} + +/* ------------------------------------------------------------------------- */ + +/* ***************** m1 = m2 ***************** */ +void cpy_m3_m3(float m1[][3], float m2[][3]) +{ + memcpy(m1[0], m2[0], 9*sizeof(float)); +} + +/* ***************** m1 = m2 ***************** */ +void cpy_m4_m4(float m1[][4], float m2[][4]) +{ + memcpy(m1[0], m2[0], 16*sizeof(float)); +} + +/* ***************** identity matrix ***************** */ +void ident_m4(float m[][4]) +{ + + m[0][0]= m[1][1]= m[2][2]= m[3][3]= 1.0; + m[0][1]= m[0][2]= m[0][3]= 0.0; + m[1][0]= m[1][2]= m[1][3]= 0.0; + m[2][0]= m[2][1]= m[2][3]= 0.0; + m[3][0]= m[3][1]= m[3][2]= 0.0; +} + + +/* ***************** m1 = m2 (pre) * m3 (post) ***************** */ +void mul_m3_m3m3(float m1[][3], float m2[][3], float m3[][3]) +{ + float m[3][3]; + + m[0][0]= m2[0][0]*m3[0][0] + m2[1][0]*m3[0][1] + m2[2][0]*m3[0][2]; + m[0][1]= m2[0][1]*m3[0][0] + m2[1][1]*m3[0][1] + m2[2][1]*m3[0][2]; + m[0][2]= m2[0][2]*m3[0][0] + m2[1][2]*m3[0][1] + m2[2][2]*m3[0][2]; + + m[1][0]= m2[0][0]*m3[1][0] + m2[1][0]*m3[1][1] + m2[2][0]*m3[1][2]; + m[1][1]= m2[0][1]*m3[1][0] + m2[1][1]*m3[1][1] + m2[2][1]*m3[1][2]; + m[1][2]= m2[0][2]*m3[1][0] + m2[1][2]*m3[1][1] + m2[2][2]*m3[1][2]; + + m[2][0]= m2[0][0]*m3[2][0] + m2[1][0]*m3[2][1] + m2[2][0]*m3[2][2]; + m[2][1]= m2[0][1]*m3[2][0] + m2[1][1]*m3[2][1] + m2[2][1]*m3[2][2]; + m[2][2]= m2[0][2]*m3[2][0] + m2[1][2]*m3[2][1] + m2[2][2]*m3[2][2]; + + cpy_m3_m3(m1, m2); +} + +/* ***************** m1 = m2 (pre) * m3 (post) ***************** */ +void mul_m4_m4m4(float m1[][4], float m2[][4], float m3[][4]) +{ + float m[4][4]; + + m[0][0]= m2[0][0]*m3[0][0] + m2[1][0]*m3[0][1] + m2[2][0]*m3[0][2] + m2[3][0]*m3[0][3]; + m[0][1]= m2[0][1]*m3[0][0] + m2[1][1]*m3[0][1] + m2[2][1]*m3[0][2] + m2[3][1]*m3[0][3]; + m[0][2]= m2[0][2]*m3[0][0] + m2[1][2]*m3[0][1] + m2[2][2]*m3[0][2] + m2[3][2]*m3[0][3]; + m[0][3]= m2[0][3]*m3[0][0] + m2[1][3]*m3[0][1] + m2[2][3]*m3[0][2] + m2[3][3]*m3[0][3]; + + m[1][0]= m2[0][0]*m3[1][0] + m2[1][0]*m3[1][1] + m2[2][0]*m3[1][2] + m2[3][0]*m3[1][3]; + m[1][1]= m2[0][1]*m3[1][0] + m2[1][1]*m3[1][1] + m2[2][1]*m3[1][2] + m2[3][1]*m3[1][3]; + m[1][2]= m2[0][2]*m3[1][0] + m2[1][2]*m3[1][1] + m2[2][2]*m3[1][2] + m2[3][2]*m3[1][3]; + m[1][3]= m2[0][3]*m3[1][0] + m2[1][3]*m3[1][1] + m2[2][3]*m3[1][2] + m2[3][3]*m3[1][3]; + + m[2][0]= m2[0][0]*m3[2][0] + m2[1][0]*m3[2][1] + m2[2][0]*m3[2][2] + m2[3][0]*m3[2][3]; + m[2][1]= m2[0][1]*m3[2][0] + m2[1][1]*m3[2][1] + m2[2][1]*m3[2][2] + m2[3][1]*m3[2][3]; + m[2][2]= m2[0][2]*m3[2][0] + m2[1][2]*m3[2][1] + m2[2][2]*m3[2][2] + m2[3][2]*m3[2][3]; + m[2][3]= m2[0][3]*m3[2][0] + m2[1][3]*m3[2][1] + m2[2][3]*m3[2][2] + m2[3][3]*m3[2][3]; + + m[3][0]= m2[0][0]*m3[3][0] + m2[1][0]*m3[3][1] + m2[2][0]*m3[3][2] + m2[3][0]*m3[3][3]; + m[3][1]= m2[0][1]*m3[3][0] + m2[1][1]*m3[3][1] + m2[2][1]*m3[3][2] + m2[3][1]*m3[3][3]; + m[3][2]= m2[0][2]*m3[3][0] + m2[1][2]*m3[3][1] + m2[2][2]*m3[3][2] + m2[3][2]*m3[3][3]; + m[3][3]= m2[0][3]*m3[3][0] + m2[1][3]*m3[3][1] + m2[2][3]*m3[3][2] + m2[3][3]*m3[3][3]; + + cpy_m4_m4(m1, m2); +} + +/* ***************** m1 = inverse(m2) ***************** */ +void inv_m3_m3(float m1[][3], float m2[][3]) +{ + short a,b; + float det; + + /* calc adjoint */ + Mat3Adj(m1, m2); + + /* then determinant old matrix! */ + det= m2[0][0]* (m2[1][1]*m2[2][2] - m2[1][2]*m2[2][1]) + -m2[1][0]* (m2[0][1]*m2[2][2] - m2[0][2]*m2[2][1]) + +m2[2][0]* (m2[0][1]*m2[1][2] - m2[0][2]*m2[1][1]); + + if(det==0.0f) det=1.0f; + det= 1.0f/det; + for(a=0;a<3;a++) { + for(b=0;b<3;b++) { + m1[a][b]*=det; + } + } +} + +/* ***************** m1 = inverse(m2) ***************** */ +int inv_m4_m4(float inverse[][4], float mat[][4]) +{ + int i, j, k; + double temp; + float tempmat[4][4]; + float max; + int maxj; + + /* Set inverse to identity */ + ident_m4(inverse); + + /* Copy original matrix so we don't mess it up */ + cpy_m4_m4(tempmat, mat); + + for(i = 0; i < 4; i++) { + /* Look for row with max pivot */ + max = ABS(tempmat[i][i]); + maxj = i; + for(j = i + 1; j < 4; j++) { + if(ABS(tempmat[j][i]) > max) { + max = ABS(tempmat[j][i]); + maxj = j; + } + } + /* Swap rows if necessary */ + if (maxj != i) { + for( k = 0; k < 4; k++) { + SWAP(float, tempmat[i][k], tempmat[maxj][k]); + SWAP(float, inverse[i][k], inverse[maxj][k]); + } + } + + temp = tempmat[i][i]; + if (temp == 0) + return 0; /* No non-zero pivot */ + for(k = 0; k < 4; k++) { + tempmat[i][k] = (float)(tempmat[i][k]/temp); + inverse[i][k] = (float)(inverse[i][k]/temp); + } + for(j = 0; j < 4; j++) { + if(j != i) { + temp = tempmat[j][i]; + for(k = 0; k < 4; k++) { + tempmat[j][k] -= (float)(tempmat[i][k]*temp); + inverse[j][k] -= (float)(inverse[i][k]*temp); + } + } + } + } + return 1; +} + +/* ***************** v1 = v2 * mat ***************** */ +void mul_v3_v3m4(float *v1, float *v2, float mat[][4]) +{ + float x, y; + + x= v2[0]; /* work with a copy, v1 can be same as v2 */ + y= v2[1]; + v1[0]= x*mat[0][0] + y*mat[1][0] + mat[2][0]*v2[2] + mat[3][0]; + v1[1]= x*mat[0][1] + y*mat[1][1] + mat[2][1]*v2[2] + mat[3][1]; + v1[2]= x*mat[0][2] + y*mat[1][2] + mat[2][2]*v2[2] + mat[3][2]; + +} + +/* moved from effect.c + test if the line starting at p1 ending at p2 intersects the triangle v0..v2 + return non zero if it does +*/ +int LineIntersectsTriangle(float p1[3], float p2[3], float v0[3], float v1[3], float v2[3], float *lambda) +{ + + float p[3], s[3], d[3], e1[3], e2[3], q[3]; + float a, f, u, v; + + VecSubf(e1, v1, v0); + VecSubf(e2, v2, v0); + VecSubf(d, p2, p1); + + Crossf(p, d, e2); + a = Inpf(e1, p); + if ((a > -0.000001) && (a < 0.000001)) return 0; + f = 1.0f/a; + + VecSubf(s, p1, v0); + + Crossf(q, s, e1); + *lambda = f * Inpf(e2, q); + if ((*lambda < 0.0)||(*lambda > 1.0)) return 0; + + u = f * Inpf(s, p); + if ((u < 0.0)||(u > 1.0)) return 0; + + v = f * Inpf(d, q); + if ((v < 0.0)||((u + v) > 1.0)) return 0; + + return 1; +} + + +/* +find closest point to p on line through l1,l2 +and return lambda, where (0 <= lambda <= 1) when cp is in the line segement l1,l2 +*/ +float lambda_cp_line_ex(float p[3], float l1[3], float l2[3], float cp[3]) +{ + float h[3],u[3],lambda; + VecSubf(u, l2, l1); + VecSubf(h, p, l1); + lambda =Inpf(u,h)/Inpf(u,u); + cp[0] = l1[0] + u[0] * lambda; + cp[1] = l1[1] + u[1] * lambda; + cp[2] = l1[2] + u[2] * lambda; + return lambda; +} +/* little sister we only need to know lambda */ +float lambda_cp_line(float p[3], float l1[3], float l2[3]) +{ + float h[3],u[3]; + VecSubf(u, l2, l1); + VecSubf(h, p, l1); + return(Inpf(u,h)/Inpf(u,u)); +} + + + +int point_in_slice(float p[3], float v1[3], float l1[3], float l2[3]) +{ +/* +what is a slice ? +some maths: +a line including l1,l2 and a point not on the line +define a subset of R3 delimeted by planes parallel to the line and orthogonal +to the (point --> line) distance vector,one plane on the line one on the point, +the room inside usually is rather small compared to R3 though still infinte +useful for restricting (speeding up) searches +e.g. all points of triangular prism are within the intersection of 3 'slices' +onother trivial case : cube +but see a 'spat' which is a deformed cube with paired parallel planes needs only 3 slices too +*/ + float h,rp[3],cp[3],q[3]; + + lambda_cp_line_ex(v1,l1,l2,cp); + VecSubf(q,cp,v1); + + VecSubf(rp,p,v1); + h=Inpf(q,rp)/Inpf(q,q); + if (h < 0.0f || h > 1.0f) return 0; + return 1; +} + +/*adult sister defining the slice planes by the origin and the normal +NOTE |normal| may not be 1 but defining the thickness of the slice*/ +int point_in_slice_as(float p[3],float origin[3],float normal[3]) +{ + float h,rp[3]; + VecSubf(rp,p,origin); + h=Inpf(normal,rp)/Inpf(normal,normal); + if (h < 0.0f || h > 1.0f) return 0; + return 1; +} + +/*mama (knowing the squared lenght of the normal)*/ +int point_in_slice_m(float p[3],float origin[3],float normal[3],float lns) +{ + float h,rp[3]; + VecSubf(rp,p,origin); + h=Inpf(normal,rp)/lns; + if (h < 0.0f || h > 1.0f) return 0; + return 1; +} + + +int point_in_tri_prism(float p[3], float v1[3], float v2[3], float v3[3]) +{ + if(!point_in_slice(p,v1,v2,v3)) return 0; + if(!point_in_slice(p,v2,v3,v1)) return 0; + if(!point_in_slice(p,v3,v1,v2)) return 0; + return 1; +} + +/* point closest to v1 on line v2-v3 in 3D */ +void PclosestVL3Dfl(float *closest, float *v1, float *v2, float *v3) +{ + float lambda, cp[3]; + + lambda= lambda_cp_line_ex(v1, v2, v3, cp); + + if(lambda <= 0.0f) + VecCopyf(closest, v2); + else if(lambda >= 1.0f) + VecCopyf(closest, v3); + else + VecCopyf(closest, cp); +} + +/* distance v1 to line-piece v2-v3 in 3D */ +float PdistVL3Dfl(float *v1, float *v2, float *v3) +{ + float closest[3]; + + PclosestVL3Dfl(closest, v1, v2, v3); + + return VecLenf(closest, v1); +} + +/********************************************************/ + +/* make a 4x4 matrix out of 3 transform components */ +/* matrices are made in the order: scale * rot * loc */ +void LocEulSizeToMat4(float mat[][4], float loc[3], float eul[3], float size[3]) +{ + float rmat[3][3], smat[3][3], tmat[3][3]; + + /* initialise new matrix */ + Mat4One(mat); + + /* make rotation + scaling part */ + EulToMat3(eul, rmat); + SizeToMat3(size, smat); + Mat3MulMat3(tmat, rmat, smat); + + /* copy rot/scale part to output matrix*/ + Mat4CpyMat3(mat, tmat); + + /* copy location to matrix */ + mat[3][0] = loc[0]; + mat[3][1] = loc[1]; + mat[3][2] = loc[2]; +} + +/* make a 4x4 matrix out of 3 transform components */ +/* matrices are made in the order: scale * rot * loc */ +void LocQuatSizeToMat4(float mat[][4], float loc[3], float quat[4], float size[3]) +{ + float rmat[3][3], smat[3][3], tmat[3][3]; + + /* initialise new matrix */ + Mat4One(mat); + + /* make rotation + scaling part */ + QuatToMat3(quat, rmat); + SizeToMat3(size, smat); + Mat3MulMat3(tmat, rmat, smat); + + /* copy rot/scale part to output matrix*/ + Mat4CpyMat3(mat, tmat); + + /* copy location to matrix */ + mat[3][0] = loc[0]; + mat[3][1] = loc[1]; + mat[3][2] = loc[2]; +} |