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
58static void normalize(float vec[3]);
59static void crossProduct(float x[3], float y[3], float ret[3]);
60#if 0 // UNUSED
61static void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride,  int dimension, float u, float retpoint[]);
62#endif
63
64static 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
75void 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 */
99void 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 */
125void 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
146void 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 */
176void 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*/
192void 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
202void 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*/
234static 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
253static 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
261