src/glu/sgi/libnurbs/interface/bezierEval.cc

   1 /*
   2 ** License Applicability. Except to the extent portions of this file are
   3 ** made subject to an alternative license as permitted in the SGI Free
   4 ** Software License B, Version 1.1 (the "License"), the contents of this
   5 ** file are subject only to the provisions of the License. You may not use
   6 ** this file except in compliance with the License. You may obtain a copy
   7 ** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
   8 ** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
   9 **
  10 ** http://oss.sgi.com/projects/FreeB
  11 **
  12 ** Note that, as provided in the License, the Software is distributed on an
  13 ** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
  14 ** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
  15 ** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
  16 ** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
  17 **
  18 ** Original Code. The Original Code is: OpenGL Sample Implementation,
  19 ** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
  20 ** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
  21 ** Copyright in any portions created by third parties is as indicated
  22 ** elsewhere herein. All Rights Reserved.
  23 **
  24 ** Additional Notice Provisions: The application programming interfaces
  25 ** established by SGI in conjunction with the Original Code are The
  26 ** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
  27 ** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
  28 ** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
  29 ** Window System(R) (Version 1.3), released October 19, 1998. This software
  30 ** was created using the OpenGL(R) version 1.2.1 Sample Implementation
  31 ** published by SGI, but has not been independently verified as being
  32 ** compliant with the OpenGL(R) version 1.2.1 Specification.
  33 **
  34 */
  35 /*
  36 */
  37
  38 #include <stdlib.h>
  39 #include <stdio.h>
  40 #include <assert.h>
  41 #include <math.h>
  42 #include "bezierEval.h"
  43
  44 #ifdef __WATCOMC__
  45 #pragma warning 14  10
  46 #endif
  47
  48 #define TOLERANCE 0.0001
  49
  50 #ifndef MAX_ORDER
  51 #define MAX_ORDER 16
  52 #endif
  53
  54 #ifndef MAX_DIMENSION
  55 #define MAX_DIMENSION 4
  56 #endif
  57
  58 static void normalize(float vec[3]);
  59 static void crossProduct(float x[3], float y[3], float ret[3]);
  60 #if 0 // UNUSED
  61 static void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retpoint[]);
  62 #endif
  63
  64 static float binomialCoefficients[8][8] = {
  65   {1,0,0,0,0,0,0,0},
  66   {1,1,0,0,0,0,0,0},
  67   {1,2,1,0,0,0,0,0},
  68   {1,3,3,1,0,0,0,0},
  69   {1,4,6,4,1,0,0,0},
  70   {1,5,10,10,5,1,0,0},
  71   {1,6,15,20,15,6,1,0},
  72   {1,7,21,35,35,21,7,1}
  73 };
  74
  75 void bezierCurveEval(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[])
  76 {
  77   float uprime = (u-u0)/(u1-u0);
  78   float *ctlptr = ctlpoints;
  79   float oneMinusX = 1.0f-uprime;
  80   float XPower = 1.0f;
  81
  82   int i,k;
  83   for(k=0; k<dimension; k++)
  84     retpoint[k] = (*(ctlptr + k));
  85
  86   for(i=1; i<order; i++){
  87     ctlptr += stride;
  88     XPower *= uprime;
  89     for(k=0; k<dimension; k++) {
  90       retpoint[k] = retpoint[k]*oneMinusX + ctlptr[k]* binomialCoefficients[order-1][i] * XPower;
  91     }
  92   }
  93 }
  94
  95
  96 #if 0 // UNUSED
  97 /*order = degree +1 >=1.
  98  */
  99 void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retpoint[])
 100 {
 101   float uprime = (u-u0)/(u1-u0);
 102   float buf[MAX_ORDER][MAX_ORDER][MAX_DIMENSION];
 103   float* ctlptr = ctlpoints;
 104   int r, i,j;
 105   for(i=0; i<order; i++) {
 106     for(j=0; j<dimension; j++)
 107       buf[0][i][j] = ctlptr[j];
 108     ctlptr += stride;
 109   }
 110   for(r=1; r<order; r++){
 111     for(i=0; i<order-r; i++) {
 112       for(j=0; j<dimension; j++)
 113         buf[r][i][j] = (1-uprime)*buf[r-1][i][j] + uprime*buf[r-1][i+1][j];
 114     }
 115   }
 116
 117   for(j=0; j<dimension; j++)
 118     retpoint[j] = buf[order-1][0][j];
 119 }
 120 #endif
 121
 122
 123 /*order = degree +1 >=1.
 124  */
 125 void bezierCurveEvalDer(float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retDer[])
 126 {
 127   int i,k;
 128   float width = u1-u0;
 129   float *ctlptr = ctlpoints;
 130
 131   float buf[MAX_ORDER][MAX_DIMENSION];
 132   if(order == 1){
 133     for(k=0; k<dimension; k++)
 134       retDer[k]=0;
 135   }
 136   for(i=0; i<order-1; i++){
 137     for(k=0; k<dimension; k++) {
 138       buf[i][k] = (ctlptr[stride+k] - ctlptr[k])*(order-1)/width;
 139     }
 140     ctlptr += stride;
 141   }
 142
 143   bezierCurveEval(u0, u1, order-1, (float*) buf, MAX_DIMENSION,  dimension, u, retDer);
 144 }
 145
 146 void bezierCurveEvalDerGen(int der, float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retDer[])
 147 {
 148   int i,k,r;
 149   float *ctlptr = ctlpoints;
 150   float width=u1-u0;
 151   float buf[MAX_ORDER][MAX_ORDER][MAX_DIMENSION];
 152   if(der<0) der=0;
 153   for(i=0; i<order; i++){
 154     for(k=0; k<dimension; k++){
 155       buf[0][i][k] = ctlptr[k];
 156     }
 157     ctlptr += stride;
 158   }
 159
 160
 161   for(r=1; r<=der; r++){
 162     for(i=0; i<order-r; i++){
 163       for(k=0; k<dimension; k++){
 164         buf[r][i][k] = (buf[r-1][i+1][k] - buf[r-1][i][k])*(order-r)/width;
 165       }
 166     }
 167   }
 168
 169   bezierCurveEval(u0, u1, order-der, (float *) (buf[der]), MAX_DIMENSION, dimension, u, retDer);
 170 }
 171
 172 /*the Bezier bivarite polynomial is:
 173  * sum[i:0,uorder-1][j:0,vorder-1] { ctlpoints[i*ustride+j*vstride] * B(i)*B(j)
 174  * where B(i) and B(j) are basis functions
 175  */
 176 void bezierSurfEvalDerGen(int uder, int vder, float u0, float u1, int uorder, float v0, float v1, int vorder, int dimension, float *ctlpoints, int ustride, int vstride, float u, float v, float ret[])
 177 {
 178   int i;
 179   float newPoints[MAX_ORDER][MAX_DIMENSION];
 180
 181   for(i=0; i<uorder; i++){
 182
 183     bezierCurveEvalDerGen(vder, v0, v1, vorder, ctlpoints+ustride*i, vstride, dimension, v, newPoints[i]);
 184
 185   }
 186
 187   bezierCurveEvalDerGen(uder, u0, u1, uorder, (float *) newPoints, MAX_DIMENSION, dimension, u, ret);
 188 }
 189
 190
 191 /*division by w is performed*/
 192 void bezierSurfEval(float u0, float u1, int uorder, float v0, float v1, int vorder, int dimension, float *ctlpoints, int ustride, int vstride, float u, float v, float ret[])
 193 {
 194   bezierSurfEvalDerGen(0, 0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, ret);
 195   if(dimension == 4) /*homogeneous*/{
 196     ret[0] /= ret[3];
 197     ret[1] /= ret[3];
 198     ret[2] /= ret[3];
 199   }
 200 }
 201
 202 void bezierSurfEvalNormal(float u0, float u1, int uorder, float v0, float v1, int vorder, int dimension, float *ctlpoints, int ustride, int vstride, float u, float v, float retNormal[])
 203 {
 204   float partialU[4];
 205   float partialV[4];
 206   assert(dimension>=3 && dimension <=4);
 207   bezierSurfEvalDerGen(1,0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, partialU);
 208   bezierSurfEvalDerGen(0,1, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, partialV);
 209
 210   if(dimension == 3){/*inhomogeneous*/
 211     crossProduct(partialU, partialV, retNormal);
 212
 213     normalize(retNormal);
 214
 215     return;
 216   }
 217   else { /*homogeneous*/
 218     float val[4]; /*the point coordinates (without derivative)*/
 219     float newPartialU[MAX_DIMENSION];
 220     float newPartialV[MAX_DIMENSION];
 221     int i;
 222     bezierSurfEvalDerGen(0,0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, val);
 223
 224     for(i=0; i<=2; i++){
 225       newPartialU[i] = partialU[i] * val[3] - val[i] * partialU[3];
 226       newPartialV[i] = partialV[i] * val[3] - val[i] * partialV[3];
 227     }
 228     crossProduct(newPartialU, newPartialV, retNormal);
 229     normalize(retNormal);
 230   }
 231 }
 232
 233 /*if size is 0, then nothing is done*/
 234 static void normalize(float vec[3])
 235 {
 236   float size = (float)sqrt(vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2]);
 237
 238   if(size < TOLERANCE)
 239     {
 240 #ifdef DEBUG
 241       fprintf(stderr, "Warning: in oglBSpline.c normal is 0\n");
 242 #endif
 243       return;
 244     }
 245   else {
 246     vec[0] = vec[0]/size;
 247     vec[1] = vec[1]/size;
 248     vec[2] = vec[2]/size;
 249   }
 250 }
 251
 252
 253 static void crossProduct(float x[3], float y[3], float ret[3])
 254 {
 255   ret[0] = x[1]*y[2] - y[1]*x[2];
 256   ret[1] = x[2]*y[0] - y[2]*x[0];
 257   ret[2] = x[0]*y[1] - y[0]*x[1];
 258
 259 }
 260