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comparison mupdf-source/thirdparty/freeglut/progs/demos/Lorenz/lorenz.c @ 3:2c135c81b16c

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MERGE: upstream PyMuPDF 1.26.4 with MuPDF 1.26.7
author Franz Glasner <fzglas.hg@dom66.de>
date Mon, 15 Sep 2025 11:44:09 +0200
parents b50eed0cc0ef
children
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0:6015a75abc2d 3:2c135c81b16c
1 /*
2 * Lorenz Strange Attractor
3 *
4 * Written by John F. Fay in honor of the "freeglut" 2.0.0 release in July 2003
5 *
6 * What it does:
7 * This program starts with two particles right next to each other. The particles
8 * move through a three-dimensional phase space governed by the following equations:
9 * dx/dt = sigma * ( y - x )
10 * dy/dt = r * x - y + x * z
11 * dz/dt = x * y + b * z
12 * These are the Lorenz equations and define the "Lorenz Attractor." Any two particles
13 * arbitrarily close together will move apart as time increases, but their tracks are
14 * confined within a region of the space.
15 *
16 * Commands:
17 * Arrow keys: Rotate the view
18 * PgUp, PgDn: Zoom in and out
19 * Mouse click: Center on the nearest point on a particle trajectory
20 *
21 * 'r'/'R': Reset the simulation
22 * 'm'/'M': Modify the Lorenz parameters (in the text window)
23 * 's'/'S': Stop (the advancement in time)
24 * 'g'/'G': Go
25 * <spacebar>: Single-step
26 * <Escape>: Quit
27 */
28
29 /* Include Files */
30 #include <stdio.h>
31 #include <stdlib.h>
32 #include <stdarg.h>
33 #include <string.h>
34 #include <math.h>
35 #include <GL/freeglut.h>
36 #ifdef _MSC_VER
37 /* DUMP MEMORY LEAKS */
38 #include <crtdbg.h>
39 #endif
40
41
42 /************************************** Defined Constants ***************************************/
43 /* Number of points to draw in the curves */
44 #define NUM_POINTS 512
45
46 /* Angle to rotate when the user presses an arrow key */
47 #define ROTATION_ANGLE 5.0
48
49 /* Amount to scale bu when the user presses PgUp or PgDn */
50 #define SCALE_FACTOR 0.8
51
52
53 /*************************************** Global Variables ***************************************/
54 /* Lorenz Attractor variables */
55 double s0 = 10.0, r0 = 28.0, b0 = 8.0/3.0 ; /* Default Lorenz attactor parameters */
56 double time_step = 0.03 ; /* Time step in the simulation */
57 double sigma = 10.0, r = 28.0, b = 8.0/3.0 ; /* Lorenz attactor parameters */
58 double red_position[NUM_POINTS][3] ; /* Path of the red point */
59 double grn_position[NUM_POINTS][3] ; /* Path of the green point */
60 int array_index ; /* Position in *_position arrays of most recent point */
61 double distance = 0.0 ; /* Distance between the two points */
62
63 /* GLUT variables */
64 double yaw = 0.0, pit = 0.0 ; /* Euler angles of the viewing rotation */
65 double scale = 1.0 ; /* Scale factor */
66 double xcen = 0.0, ycen = 0.0, zcen = 0.0 ; /* Coordinates of the point looked at */
67
68 int animate = 1 ; /* 0 - stop, 1 = go, 2 = single-step */
69
70
71 /******************************************* Functions ******************************************/
72
73 /* The Lorenz Attractor */
74 void calc_deriv ( double position[3], double deriv[3] )
75 {
76 /* Calculate the Lorenz attractor derivatives */
77 deriv[0] = sigma * ( position[1] - position[0] ) ;
78 deriv[1] = ( r + position[2] ) * position[0] - position[1] ;
79 deriv[2] = -position[0] * position[1] - b * position[2] ;
80 }
81
82 void advance_in_time ( double time_step, double position[3], double new_position[3] )
83 {
84 /* Move a point along the Lorenz attractor */
85 double deriv0[3], deriv1[3], deriv2[3], deriv3[3] ;
86 int i ;
87 memcpy ( new_position, position, 3 * sizeof(double) ) ; /* Save the present values */
88
89 /* First pass in a Fourth-Order Runge-Kutta integration method */
90 calc_deriv ( position, deriv0 ) ;
91 for ( i = 0; i < 3; i++ )
92 new_position[i] = position[i] + 0.5 * time_step * deriv0[i] ;
93
94 /* Second pass */
95 calc_deriv ( new_position, deriv1 ) ;
96 for ( i = 0; i < 3; i++ )
97 new_position[i] = position[i] + 0.5 * time_step * deriv1[i] ;
98
99 /* Third pass */
100 calc_deriv ( position, deriv2 ) ;
101 for ( i = 0; i < 3; i++ )
102 new_position[i] = position[i] + time_step * deriv2[i] ;
103
104 /* Second pass */
105 calc_deriv ( new_position, deriv3 ) ;
106 for ( i = 0; i < 3; i++ )
107 new_position[i] = position[i] + 0.1666666666666666667 * time_step *
108 ( deriv0[i] + 2.0 * ( deriv1[i] + deriv2[i] ) + deriv3[i] ) ;
109 }
110
111 static void
112 checkedFGets ( char *s, int size, FILE *stream )
113 {
114 if ( fgets ( s, size, stream ) == NULL ) {
115 fprintf ( stderr, "fgets failed\n");
116 exit ( EXIT_FAILURE );
117 }
118 }
119
120
121 /* GLUT callbacks */
122
123 #define INPUT_LINE_LENGTH 80
124
125 void key_cb ( unsigned char key, int x, int y )
126 {
127 int i ;
128 char inputline [ INPUT_LINE_LENGTH ] ;
129
130 switch ( key )
131 {
132 case 'r' : case 'R' : /* Reset the simulation */
133 /* Reset the Lorenz parameters */
134 sigma = s0 ;
135 b = b0 ;
136 r = r0 ;
137 /* Set an initial position */
138 red_position[0][0] = (double)rand() / (double)RAND_MAX ;
139 red_position[0][1] = (double)rand() / (double)RAND_MAX ;
140 red_position[0][2] = (double)rand() / (double)RAND_MAX ;
141 grn_position[0][0] = (double)rand() / (double)RAND_MAX ;
142 grn_position[0][1] = (double)rand() / (double)RAND_MAX ;
143 grn_position[0][2] = (double)rand() / (double)RAND_MAX ;
144 array_index = 0 ;
145 /* Initialize the arrays */
146 for ( i = 1; i < NUM_POINTS; i++ )
147 {
148 memcpy ( red_position[i], red_position[0], 3 * sizeof(double) ) ;
149 memcpy ( grn_position[i], grn_position[0], 3 * sizeof(double) ) ;
150 }
151
152 break ;
153
154 case 'm' : case 'M' : /* Modify the Lorenz parameters */
155 printf ( "Please enter new value for <sigma> (default %f, currently %f): ", s0, sigma ) ;
156 checkedFGets ( inputline, sizeof ( inputline ), stdin ) ;
157 sscanf ( inputline, "%lf", &sigma ) ;
158
159 printf ( "Please enter new value for <b> (default %f, currently %f): ", b0, b ) ;
160 checkedFGets ( inputline, sizeof ( inputline ), stdin ) ;
161 sscanf ( inputline, "%lf", &b ) ;
162
163 printf ( "Please enter new value for <r> (default %f, currently %f): ", r0, r ) ;
164 checkedFGets ( inputline, sizeof ( inputline ), stdin ) ;
165 sscanf ( inputline, "%lf", &r ) ;
166
167 break ;
168
169 case 's' : case 'S' : /* Stop the animation */
170 animate = 0 ;
171 break ;
172
173 case 'g' : case 'G' : /* Start the animation */
174 animate = 1 ;
175 break ;
176
177 case ' ' : /* Spacebar: Single step */
178 animate = 2 ;
179 break ;
180
181 case 27 : /* Escape key */
182 glutLeaveMainLoop () ;
183 break ;
184 }
185 }
186
187 void special_cb ( int key, int x, int y )
188 {
189 switch ( key )
190 {
191 case GLUT_KEY_UP : /* Rotate up a little */
192 glRotated ( ROTATION_ANGLE, 0.0, 1.0, 0.0 ) ;
193 break ;
194
195 case GLUT_KEY_DOWN : /* Rotate down a little */
196 glRotated ( -ROTATION_ANGLE, 0.0, 1.0, 0.0 ) ;
197 break ;
198
199 case GLUT_KEY_LEFT : /* Rotate left a little */
200 glRotated ( ROTATION_ANGLE, 0.0, 0.0, 1.0 ) ;
201 break ;
202
203 case GLUT_KEY_RIGHT : /* Rotate right a little */
204 glRotated ( -ROTATION_ANGLE, 0.0, 0.0, 1.0 ) ;
205 break ;
206
207 case GLUT_KEY_PAGE_UP : /* Zoom in a little */
208 glScaled ( 1.0 / SCALE_FACTOR, 1.0 / SCALE_FACTOR, 1.0 / SCALE_FACTOR ) ;
209 break ;
210
211 case GLUT_KEY_PAGE_DOWN : /* Zoom out a little */
212 glScaled ( SCALE_FACTOR, SCALE_FACTOR, SCALE_FACTOR ) ;
213 break ;
214 }
215
216 glutPostRedisplay () ;
217 }
218
219 void mouse_cb ( int button, int updown, int x, int y )
220 {
221 if ( updown == GLUT_DOWN )
222 {
223 /*double dist = 1.0e20 ; A very large number */
224 /* The idea here is that we go into "pick" mode and pick the nearest point
225 to the mouse click position. Unfortunately I don't have the time to implement
226 it at the moment. */
227 }
228 }
229
230 void draw_curve ( int index, double position [ NUM_POINTS ][3] )
231 {
232 int i = index ;
233
234 glBegin ( GL_LINE_STRIP ) ;
235 do
236 {
237 i = ( i == NUM_POINTS-1 ) ? 0 : i + 1 ;
238 glVertex3dv ( position[i] ) ;
239 }
240 while ( i != index ) ;
241
242 glEnd () ;
243 }
244
245 void bitmapPrintf (const char *fmt, ...)
246 {
247 static char buf[256];
248 va_list args;
249
250 va_start(args, fmt);
251 #if defined(WIN32) && !defined(__CYGWIN__)
252 (void) _vsnprintf (buf, sizeof(buf), fmt, args);
253 #else
254 (void) vsnprintf (buf, sizeof(buf), fmt, args);
255 #endif
256 va_end(args);
257 glutBitmapString ( GLUT_BITMAP_HELVETICA_12, (unsigned char*)buf ) ;
258 }
259
260 void display_cb ( void )
261 {
262 glClear ( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ) ;
263
264 glColor3d ( 1.0, 1.0, 1.0 ) ; /* White */
265 /* Draw some axes */
266 glBegin ( GL_LINES ) ;
267 glVertex3d ( 0.0, 0.0, 0.0 ) ;
268 glVertex3d ( 2.0, 0.0, 0.0 ) ;
269 glVertex3d ( 0.0, 0.0, 0.0 ) ;
270 glVertex3d ( 0.0, 1.0, 0.0 ) ;
271 glVertex3d ( 0.0, 0.0, 0.0 ) ;
272 glVertex3d ( 0.0, 0.0, 1.0 ) ;
273 glEnd () ;
274
275 glColor3d ( 1.0, 0.0, 0.0 ) ; /* Red */
276 draw_curve ( array_index, red_position ) ;
277
278 glColor3d ( 0.0, 1.0, 0.0 ) ; /* Green */
279 draw_curve ( array_index, grn_position ) ;
280
281 /* Print the distance between the two points */
282 glColor3d ( 1.0, 1.0, 1.0 ) ; /* White */
283 glRasterPos2i ( 1, 1 ) ;
284 bitmapPrintf ( "Distance: %10.6f", distance ) ;
285
286 glutSwapBuffers();
287 }
288
289 void reshape_cb ( int width, int height )
290 {
291 float ar;
292 glViewport ( 0, 0, width, height ) ;
293 glMatrixMode ( GL_PROJECTION ) ;
294 glLoadIdentity () ;
295 ar = (float) width / (float) height ;
296 glFrustum ( -ar, ar, -1.0, 1.0, 10.0, 100.0 ) ;
297 glMatrixMode ( GL_MODELVIEW ) ;
298 glLoadIdentity () ;
299 xcen = 0.0 ;
300 ycen = 0.0 ;
301 zcen = 0.0 ;
302 glTranslated ( xcen, ycen, zcen - 50.0 ) ;
303 }
304
305
306 void timer_cb ( int value )
307 {
308 /* Function called at regular intervals to update the positions of the points */
309 double deltax, deltay, deltaz ;
310 int new_index = array_index + 1 ;
311
312 /* Set the next timed callback */
313 glutTimerFunc ( 30, timer_cb, 0 ) ;
314
315 if ( animate > 0 )
316 {
317 if ( new_index == NUM_POINTS ) new_index = 0 ;
318 advance_in_time ( time_step, red_position[array_index], red_position[new_index] ) ;
319 advance_in_time ( time_step, grn_position[array_index], grn_position[new_index] ) ;
320 array_index = new_index ;
321
322 deltax = red_position[array_index][0] - grn_position[array_index][0] ;
323 deltay = red_position[array_index][1] - grn_position[array_index][1] ;
324 deltaz = red_position[array_index][2] - grn_position[array_index][2] ;
325 distance = sqrt ( deltax * deltax + deltay * deltay + deltaz * deltaz ) ;
326
327 if ( animate == 2 ) animate = 0 ;
328 }
329
330 glutPostRedisplay () ;
331 }
332
333
334
335 /* The Main Program */
336
337 int main ( int argc, char *argv[] )
338 {
339 int pargc = argc ;
340
341 /* Initialize the random number generator */
342 srand ( 1023 ) ;
343
344 /* Set up the OpenGL parameters */
345 glEnable ( GL_DEPTH_TEST ) ;
346 glClearColor ( 0.0, 0.0, 0.0, 0.0 ) ;
347 glClearDepth ( 1.0 ) ;
348
349 /* Initialize GLUT */
350 glutInitWindowSize ( 600, 600 ) ;
351 glutInit ( &pargc, argv ) ;
352 glutInitDisplayMode ( GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH ) ;
353
354 /* Create the window */
355 glutCreateWindow ( "Lorenz Attractor" ) ;
356 glutKeyboardFunc ( key_cb ) ;
357 glutMouseFunc ( mouse_cb ) ;
358 glutSpecialFunc ( special_cb ) ;
359 glutDisplayFunc ( display_cb ) ;
360 glutReshapeFunc ( reshape_cb ) ;
361 glutTimerFunc ( 30, timer_cb, 0 ) ;
362
363 /* Initialize the attractor: The easiest way is to call the keyboard callback with an
364 * argument of 'r' for Reset.
365 */
366 key_cb ( 'r', 0, 0 ) ;
367
368 /* Enter the GLUT main loop */
369 glutMainLoop () ;
370
371 #ifdef _MSC_VER
372 /* DUMP MEMORY LEAK INFORMATION */
373 _CrtDumpMemoryLeaks () ;
374 #endif
375
376 return 0 ;
377 }
378