Synchronize with trunk's revision r57629.
[reactos.git] / dll / opengl / glu32 / src / 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