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 ** $Date: 2001/11/29 16:16:55 $ $Revision: 1.2 $
  35 */
  36 /*
  37 ** $Header: /home/krh/git/sync/mesa-cvs-repo/Mesa/src/glu/sgi/libnurbs/interface/bezierEval.cc,v 1.2 2001/11/29 16:16:55 kschultz Exp $
  38 */
  39
  40 #include <stdlib.h>
  41 #include <stdio.h>
  42 #include <assert.h>
  43 #include <math.h>
  44 #include "bezierEval.h"
  45
  46 #define TOLERANCE 0.0001
  47
  48 #ifndef MAX_ORDER
  49 #define MAX_ORDER 16
  50 #endif
  51
  52 #ifndef MAX_DIMENSION
  53 #define MAX_DIMENSION 4
  54 #endif
  55
  56 static void normalize(float vec[3]);
  57 static void crossProduct(float x[3], float y[3], float ret[3]);
  58 static void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retpoint[]);
  59
  60 static float binomialCoefficients[8][8] = {
  61   {1,0,0,0,0,0,0,0},
  62   {1,1,0,0,0,0,0,0},
  63   {1,2,1,0,0,0,0,0},
  64   {1,3,3,1,0,0,0,0},
  65   {1,4,6,4,1,0,0,0},
  66   {1,5,10,10,5,1,0,0},
  67   {1,6,15,20,15,6,1,0},
  68   {1,7,21,35,35,21,7,1}
  69 };
  70
  71 void bezierCurveEval(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[])
  72 {
  73   float uprime = (u-u0)/(u1-u0);
  74   float *ctlptr = ctlpoints;
  75   float oneMinusX = 1.0f-uprime;
  76   float XPower = 1.0f;
  77
  78   int i,k;
  79   for(k=0; k<dimension; k++)
  80     retpoint[k] = (*(ctlptr + k));
  81
  82   for(i=1; i<order; i++){
  83     ctlptr += stride;
  84     XPower *= uprime;
  85     for(k=0; k<dimension; k++) {
  86       retpoint[k] = retpoint[k]*oneMinusX + ctlptr[k]* binomialCoefficients[order-1][i] * XPower;
  87     }
  88   }
  89 }
  90
  91
  92
  93 /*order = degree +1 >=1.
  94  */
  95 void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retpoint[])
  96 {
  97   float uprime = (u-u0)/(u1-u0);
  98   float buf[MAX_ORDER][MAX_ORDER][MAX_DIMENSION];
  99   float* ctlptr = ctlpoints;
 100   int r, i,j;
 101   for(i=0; i<order; i++) {
 102     for(j=0; j<dimension; j++)
 103       buf[0][i][j] = ctlptr[j];
 104     ctlptr += stride;
 105   }
 106   for(r=1; r<order; r++){
 107     for(i=0; i<order-r; i++) {
 108       for(j=0; j<dimension; j++)
 109         buf[r][i][j] = (1-uprime)*buf[r-1][i][j] + uprime*buf[r-1][i+1][j];
 110     }
 111   }
 112
 113   for(j=0; j<dimension; j++)
 114     retpoint[j] = buf[order-1][0][j];
 115 }
 116
 117
 118
 119 /*order = degree +1 >=1.
 120  */
 121 void bezierCurveEvalDer(float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retDer[])
 122 {
 123   int i,k;
 124   float width = u1-u0;
 125   float *ctlptr = ctlpoints;
 126
 127   float buf[MAX_ORDER][MAX_DIMENSION];
 128   if(order == 1){
 129     for(k=0; k<dimension; k++)
 130       retDer[k]=0;
 131   }
 132   for(i=0; i<order-1; i++){
 133     for(k=0; k<dimension; k++) {
 134       buf[i][k] = (ctlptr[stride+k] - ctlptr[k])*(order-1)/width;
 135     }
 136     ctlptr += stride;
 137   }
 138
 139   bezierCurveEval(u0, u1, order-1, (float*) buf, MAX_DIMENSION,  dimension, u, retDer);
 140 }
 141
 142 void bezierCurveEvalDerGen(int der, float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retDer[])
 143 {
 144   int i,k,r;
 145   float *ctlptr = ctlpoints;
 146   float width=u1-u0;
 147   float buf[MAX_ORDER][MAX_ORDER][MAX_DIMENSION];
 148   if(der<0) der=0;
 149   for(i=0; i<order; i++){
 150     for(k=0; k<dimension; k++){
 151       buf[0][i][k] = ctlptr[k];
 152     }
 153     ctlptr += stride;
 154   }
 155
 156
 157   for(r=1; r<=der; r++){
 158     for(i=0; i<order-r; i++){
 159       for(k=0; k<dimension; k++){
 160         buf[r][i][k] = (buf[r-1][i+1][k] - buf[r-1][i][k])*(order-r)/width;
 161       }
 162     }
 163   }
 164
 165   bezierCurveEval(u0, u1, order-der, (float *) (buf[der]), MAX_DIMENSION, dimension, u, retDer);
 166 }
 167
 168 /*the Bezier bivarite polynomial is:
 169  * sum[i:0,uorder-1][j:0,vorder-1] { ctlpoints[i*ustride+j*vstride] * B(i)*B(j)
 170  * where B(i) and B(j) are basis functions
 171  */
 172 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[])
 173 {
 174   int i;
 175   float newPoints[MAX_ORDER][MAX_DIMENSION];
 176
 177   for(i=0; i<uorder; i++){
 178
 179     bezierCurveEvalDerGen(vder, v0, v1, vorder, ctlpoints+ustride*i, vstride, dimension, v, newPoints[i]);
 180
 181   }
 182
 183   bezierCurveEvalDerGen(uder, u0, u1, uorder, (float *) newPoints, MAX_DIMENSION, dimension, u, ret);
 184 }
 185
 186
 187 /*division by w is performed*/
 188 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[])
 189 {
 190   bezierSurfEvalDerGen(0, 0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, ret);
 191   if(dimension == 4) /*homogeneous*/{
 192     ret[0] /= ret[3];
 193     ret[1] /= ret[3];
 194     ret[2] /= ret[3];
 195   }
 196 }
 197
 198 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[])
 199 {
 200   float partialU[4];
 201   float partialV[4];
 202   assert(dimension>=3 && dimension <=4);
 203   bezierSurfEvalDerGen(1,0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, partialU);
 204   bezierSurfEvalDerGen(0,1, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, partialV);
 205
 206   if(dimension == 3){/*inhomogeneous*/
 207     crossProduct(partialU, partialV, retNormal);
 208
 209     normalize(retNormal);
 210
 211     return;
 212   }
 213   else { /*homogeneous*/
 214     float val[4]; /*the point coordinates (without derivative)*/
 215     float newPartialU[MAX_DIMENSION];
 216     float newPartialV[MAX_DIMENSION];
 217     int i;
 218     bezierSurfEvalDerGen(0,0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, val);
 219
 220     for(i=0; i<=2; i++){
 221       newPartialU[i] = partialU[i] * val[3] - val[i] * partialU[3];
 222       newPartialV[i] = partialV[i] * val[3] - val[i] * partialV[3];
 223     }
 224     crossProduct(newPartialU, newPartialV, retNormal);
 225     normalize(retNormal);
 226   }
 227 }
 228
 229 /*if size is 0, then nothing is done*/
 230 static void normalize(float vec[3])
 231 {
 232   float size = (float)sqrt(vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2]);
 233
 234   if(size < TOLERANCE)
 235     {
 236 #ifdef DEBUG
 237       fprintf(stderr, "Warning: in oglBSpline.c normal is 0\n");
 238 #endif
 239       return;
 240     }
 241   else {
 242     vec[0] = vec[0]/size;
 243     vec[1] = vec[1]/size;
 244     vec[2] = vec[2]/size;
 245   }
 246 }
 247
 248
 249 static void crossProduct(float x[3], float y[3], float ret[3])
 250 {
 251   ret[0] = x[1]*y[2] - y[1]*x[2];
 252   ret[1] = x[2]*y[0] - y[2]*x[0];
 253   ret[2] = x[0]*y[1] - y[0]*x[1];
 254
 255 }
 256