ReactOS 0.4.15-dev-7660-g0086d05
bezierEval.cc
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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);
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
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;
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
_STLP_DECLSPEC complex< float > _STLP_CALL sqrt(const complex< float > &)
Definition: complex.cpp:188
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[])
Definition: bezierEval.cc:176
#define TOLERANCE
Definition: bezierEval.cc:48
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[])
Definition: bezierEval.cc:202
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[])
Definition: bezierEval.cc:192
#define MAX_DIMENSION
Definition: bezierEval.cc:55
void bezierCurveEval(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retpoint[])
Definition: bezierEval.cc:75
static void normalize(float vec[3])
Definition: bezierEval.cc:234
static void crossProduct(float x[3], float y[3], float ret[3])
Definition: bezierEval.cc:253
#define MAX_ORDER
Definition: bezierEval.cc:51
void bezierCurveEvalDerGen(int der, float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retDer[])
Definition: bezierEval.cc:146
void bezierCurveEvalDer(float u0, float u1, int order, float *ctlpoints, int stride, int dimension, float u, float retDer[])
Definition: bezierEval.cc:125
static float binomialCoefficients[8][8]
Definition: bezierEval.cc:64
#define assert(x)
Definition: debug.h:53
FT_Vector * vec
Definition: ftbbox.c:448
GLint GLint GLint GLint GLint x
Definition: gl.h:1548
const GLdouble * v
Definition: gl.h:2040
GLint GLint GLint GLint GLint GLint y
Definition: gl.h:1548
GLdouble GLdouble GLdouble r
Definition: gl.h:2055
GLint GLint GLsizei width
Definition: gl.h:1546
GLsizeiptr size
Definition: glext.h:5919
GLdouble GLdouble GLint ustride
Definition: glext.h:8308
GLsizei stride
Definition: glext.h:5848
GLdouble GLdouble GLint GLint uorder
Definition: glext.h:8308
GLenum GLuint GLenum GLsizei const GLchar * buf
Definition: glext.h:7751
GLuint GLfloat * val
Definition: glext.h:7180
GLfloat v0
Definition: glext.h:6061
GLdouble GLdouble GLint GLint GLdouble GLdouble GLint GLint vorder
Definition: glext.h:8308
GLuint GLdouble GLdouble GLint GLint order
Definition: glext.h:11194
GLfloat GLfloat v1
Definition: glext.h:6062
GLdouble u1
Definition: glext.h:8308
GLdouble GLdouble GLint GLint GLdouble GLdouble GLint vstride
Definition: glext.h:8308
GLsizei GLenum const GLvoid GLsizei GLenum GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLint GLint GLint GLshort GLshort GLshort GLubyte GLubyte GLubyte GLuint GLuint GLuint GLushort GLushort GLushort GLbyte GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLfloat GLint GLint GLint GLint GLshort GLshort GLshort GLshort GLubyte GLubyte GLubyte GLubyte GLuint GLuint GLuint GLuint GLushort GLushort GLushort GLushort GLboolean const GLdouble const GLfloat const GLint const GLshort const GLbyte const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLdouble const GLfloat const GLfloat const GLint const GLint const GLshort const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort GLenum GLenum GLenum GLfloat GLenum GLint GLenum GLenum GLenum GLfloat GLenum GLenum GLint GLenum GLfloat GLenum GLint GLint GLushort GLenum GLenum GLfloat GLenum GLenum GLint GLfloat const GLubyte GLenum GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLint GLint GLsizei GLsizei GLint GLenum GLenum const GLvoid GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLenum const GLdouble GLenum GLenum const GLfloat GLenum GLenum const GLint GLsizei GLuint GLfloat GLuint GLbitfield GLfloat GLint GLuint GLboolean GLenum GLfloat GLenum GLbitfield GLenum GLfloat GLfloat GLint GLint const GLfloat GLenum GLfloat GLfloat GLint GLint GLfloat GLfloat GLint GLint const GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat const GLdouble const GLfloat const GLdouble const GLfloat GLint i
Definition: glfuncs.h:248
GLsizei GLenum const GLvoid GLsizei GLenum GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLint GLint GLint GLshort GLshort GLshort GLubyte GLubyte GLubyte GLuint GLuint GLuint GLushort GLushort GLushort GLbyte GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLfloat GLint GLint GLint GLint GLshort GLshort GLshort GLshort GLubyte GLubyte GLubyte GLubyte GLuint GLuint GLuint GLuint GLushort GLushort GLushort GLushort GLboolean const GLdouble const GLfloat const GLint const GLshort const GLbyte const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLdouble const GLfloat const GLfloat const GLint const GLint const GLshort const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort GLenum GLenum GLenum GLfloat GLenum GLint GLenum GLenum GLenum GLfloat GLenum GLenum GLint GLenum GLfloat GLenum GLint GLint GLushort GLenum GLenum GLfloat GLenum GLenum GLint GLfloat const GLubyte GLenum GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLint GLint GLsizei GLsizei GLint GLenum GLenum const GLvoid GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLenum const GLdouble GLenum GLenum const GLfloat GLenum GLenum const GLint GLsizei GLuint GLfloat GLuint GLbitfield GLfloat GLint GLuint GLboolean GLenum GLfloat GLenum GLbitfield GLenum GLfloat GLfloat GLint GLint const GLfloat GLenum GLfloat GLfloat GLint GLint GLfloat GLfloat GLint GLint const GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat const GLdouble * u
Definition: glfuncs.h:240
GLsizei GLenum const GLvoid GLsizei GLenum GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLint GLint GLint GLshort GLshort GLshort GLubyte GLubyte GLubyte GLuint GLuint GLuint GLushort GLushort GLushort GLbyte GLbyte GLbyte GLbyte GLdouble GLdouble GLdouble GLdouble GLfloat GLfloat GLfloat GLfloat GLint GLint GLint GLint GLshort GLshort GLshort GLshort GLubyte GLubyte GLubyte GLubyte GLuint GLuint GLuint GLuint GLushort GLushort GLushort GLushort GLboolean const GLdouble const GLfloat const GLint const GLshort const GLbyte const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLdouble const GLfloat const GLfloat const GLint const GLint const GLshort const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort const GLdouble const GLfloat const GLint const GLshort GLenum GLenum GLenum GLfloat GLenum GLint GLenum GLenum GLenum GLfloat GLenum GLenum GLint GLenum GLfloat GLenum GLint GLint GLushort GLenum GLenum GLfloat GLenum GLenum GLint GLfloat const GLubyte GLenum GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLint GLint GLsizei GLsizei GLint GLenum GLenum const GLvoid GLenum GLenum const GLfloat GLenum GLenum const GLint GLenum GLenum const GLdouble GLenum GLenum const GLfloat GLenum GLenum const GLint GLsizei GLuint GLfloat GLuint GLbitfield GLfloat GLint GLuint GLboolean GLenum GLfloat GLenum GLbitfield GLenum GLfloat GLfloat GLint GLint const GLfloat GLenum GLfloat GLfloat GLint GLint GLfloat GLfloat GLint GLint const GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat GLint GLfloat GLfloat const GLdouble const GLfloat const GLdouble const GLfloat GLint GLint GLint j
Definition: glfuncs.h:250
#define stderr
Definition: stdio.h:100
_Check_return_opt_ _CRTIMP int __cdecl fprintf(_Inout_ FILE *_File, _In_z_ _Printf_format_string_ const char *_Format,...)
static float(__cdecl *square_half_float)(float x
int k
Definition: mpi.c:3369
int ret