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:
10 ** http://oss.sgi.com/projects/FreeB
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.
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.
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.
42 #include "bezierEval.h"
48 #define TOLERANCE 0.0001
55 #define MAX_DIMENSION 4
58 static void normalize(float vec[3]);
59 static void crossProduct(float x[3], float y[3], float ret[3]);
61 static void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[]);
64 static float binomialCoefficients[8][8] = {
75 void bezierCurveEval(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[])
77 float uprime = (u-u0)/(u1-u0);
78 float *ctlptr = ctlpoints;
79 float oneMinusX = 1.0f-uprime;
83 for(k=0; k<dimension; k++)
84 retpoint[k] = (*(ctlptr + k));
86 for(i=1; i<order; i++){
89 for(k=0; k<dimension; k++) {
90 retpoint[k] = retpoint[k]*oneMinusX + ctlptr[k]* binomialCoefficients[order-1][i] * XPower;
97 /*order = degree +1 >=1.
99 void bezierCurveEvalfast(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[])
101 float uprime = (u-u0)/(u1-u0);
102 float buf[MAX_ORDER][MAX_ORDER][MAX_DIMENSION];
103 float* ctlptr = ctlpoints;
105 for(i=0; i<order; i++) {
106 for(j=0; j<dimension; j++)
107 buf[0][i][j] = ctlptr[j];
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];
117 for(j=0; j<dimension; j++)
118 retpoint[j] = buf[order-1][0][j];
123 /*order = degree +1 >=1.
125 void bezierCurveEvalDer(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retDer[])
129 float *ctlptr = ctlpoints;
131 float buf[MAX_ORDER][MAX_DIMENSION];
133 for(k=0; k<dimension; k++)
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;
143 bezierCurveEval(u0, u1, order-1, (float*) buf, MAX_DIMENSION, dimension, u, retDer);
146 void bezierCurveEvalDerGen(int der, float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retDer[])
149 float *ctlptr = ctlpoints;
151 float buf[MAX_ORDER][MAX_ORDER][MAX_DIMENSION];
153 for(i=0; i<order; i++){
154 for(k=0; k<dimension; k++){
155 buf[0][i][k] = ctlptr[k];
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;
169 bezierCurveEval(u0, u1, order-der, (float *) (buf[der]), MAX_DIMENSION, dimension, u, retDer);
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
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[])
179 float newPoints[MAX_ORDER][MAX_DIMENSION];
181 for(i=0; i<uorder; i++){
183 bezierCurveEvalDerGen(vder, v0, v1, vorder, ctlpoints+ustride*i, vstride, dimension, v, newPoints[i]);
187 bezierCurveEvalDerGen(uder, u0, u1, uorder, (float *) newPoints, MAX_DIMENSION, dimension, u, ret);
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[])
194 bezierSurfEvalDerGen(0, 0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, ret);
195 if(dimension == 4) /*homogeneous*/{
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[])
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);
210 if(dimension == 3){/*inhomogeneous*/
211 crossProduct(partialU, partialV, retNormal);
213 normalize(retNormal);
217 else { /*homogeneous*/
218 float val[4]; /*the point coordinates (without derivative)*/
219 float newPartialU[MAX_DIMENSION];
220 float newPartialV[MAX_DIMENSION];
222 bezierSurfEvalDerGen(0,0, u0, u1, uorder, v0, v1, vorder, dimension, ctlpoints, ustride, vstride, u, v, val);
225 newPartialU[i] = partialU[i] * val[3] - val[i] * partialU[3];
226 newPartialV[i] = partialV[i] * val[3] - val[i] * partialV[3];
228 crossProduct(newPartialU, newPartialV, retNormal);
229 normalize(retNormal);
233 /*if size is 0, then nothing is done*/
234 static void normalize(float vec[3])
236 float size = (float)sqrt(vec[0]*vec[0] + vec[1]*vec[1] + vec[2]*vec[2]);
241 fprintf(stderr, "Warning: in oglBSpline.c normal is 0\n");
246 vec[0] = vec[0]/size;
247 vec[1] = vec[1]/size;
248 vec[2] = vec[2]/size;
253 static void crossProduct(float x[3], float y[3], float ret[3])
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];