3 * Program to draw a fractal by Michael Barnsley's deterministic algorithm.
5 * (1) Define the affine transformations (of the form r(i+1) = A r(i) + b )
6 * (2) Find the stationary point for each transformation
8 * - If you are at the lowest level, draw lines connecting all the stationary points
9 * - If not, call the draw function recursively with each affine transformation applied
14 * +,- - increment/decrement number of levels
15 * PgUp, PgDn - increase/decrease scaling
16 * Arrow keys - translate viewing section
21 #include <GL/freeglut.h>
28 double a00, a01, a10, a11 ; /* Transformation matrix */
29 double b0, b1 ; /* Constant vector added on */
30 double statx, staty ; /* Coordinates of the stationary point */
34 /* Number of levels to draw the fractal */
35 static int num_levels = 0 ;
37 /* The definition of the fractal */
38 static int num_trans ;
39 static AffineTrans *affine ;
41 /* the window title */
42 char window_title [ 80 ] ;
44 /* The amount the view is translated and scaled */
45 double xwin = 0.0, ywin = 0.0 ;
46 double scale_factor = 1.0 ;
48 static void draw_level ( int num, double m00, double m01, double m10, double m11, double n0, double n1 )
50 /* Draw a fractal transformed by "M", "N" as passed in */
55 double x0 = m00 * affine[0].statx + m01 * affine[0].staty + n0 ;
56 double y0 = m10 * affine[0].statx + m11 * affine[0].staty + n1 ;
58 for ( i = 1; i < num_trans; i++ )
60 double x1 = m00 * affine[i].statx + m01 * affine[i].staty + n0 ;
61 double y1 = m10 * affine[i].statx + m11 * affine[i].staty + n1 ;
63 glVertex2d ( x0, y0 ) ;
64 glVertex2d ( x1, y1 ) ;
72 /* Map each affine transformation in the fractal through the one passed in and call "draw_level" */
74 for ( i = 0; i < num_trans; i++ )
76 draw_level ( num-1, m00*affine[i].a00+m01*affine[i].a10, m00*affine[i].a01+m01*affine[i].a11,
77 m10*affine[i].a00+m11*affine[i].a10, m10*affine[i].a01+m11*affine[i].a11,
78 m00*affine[i].b0 +m01*affine[i].b1 + n0, m10*affine[i].b0 +m11*affine[i].b1 + n1 ) ;
86 glClear( GL_COLOR_BUFFER_BIT );
90 glScalef(2.5, 2.5, 2.5);
92 glColor4f(0.0, 0.0, 0.0, 1.0);
93 glBegin ( GL_LINES ) ;
94 draw_level ( num_levels, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0 );
102 Reshape(int width, int height)
105 glViewport ( 0, 0, width, height ) ;
106 glMatrixMode ( GL_PROJECTION ) ;
108 ar = (float) width / (float) height ;
110 glFrustum ( -ar, ar, -1.0, 1.0, 2.0, 100.0 ) ;
112 glFrustum ( -1.0, 1.0, -1/ar, 1/ar, 2.0, 100.0 );
113 glMatrixMode ( GL_MODELVIEW ) ;
117 glTranslated ( xwin, ywin, -5.0 ) ;
121 Key(unsigned char key, int x, int y)
123 int need_redisplay = 1;
126 case 27: /* Escape key */
127 glutLeaveMainLoop () ;
135 if ( num_levels > 0 )
139 case 'r' : case 'R' :
140 glMatrixMode ( GL_MODELVIEW ) ;
144 glTranslated ( xwin, ywin, -5.0 ) ;
156 Special(int key, int x, int y)
158 int need_redisplay = 1;
162 glMatrixMode ( GL_MODELVIEW ) ;
163 ywin += 0.1 * scale_factor ;
164 glTranslated ( 0.0, 0.1 * scale_factor, 0.0 ) ;
168 glMatrixMode ( GL_MODELVIEW ) ;
169 ywin -= 0.1 * scale_factor ;
170 glTranslated ( 0.0, -0.1 * scale_factor, 0.0 ) ;
174 glMatrixMode ( GL_MODELVIEW ) ;
175 xwin -= 0.1 * scale_factor ;
176 glTranslated ( -0.1 * scale_factor, 0.0, 0.0 ) ;
179 case GLUT_KEY_RIGHT :
180 glMatrixMode ( GL_MODELVIEW ) ;
181 xwin += 0.1 * scale_factor ;
182 glTranslated ( 0.1 * scale_factor, 0.0, 0.0 ) ;
185 case GLUT_KEY_PAGE_UP :
186 glMatrixMode ( GL_MODELVIEW ) ;
187 glTranslated ( -xwin, -ywin, 0.0 ) ;
188 glScaled ( 1.25, 1.25, 1.25 ) ;
189 glTranslated ( xwin, ywin, 0.0 ) ;
190 scale_factor *= 0.8 ;
193 case GLUT_KEY_PAGE_DOWN :
194 glMatrixMode ( GL_MODELVIEW ) ;
195 glTranslated ( -xwin, -ywin, 0.0 ) ;
196 glScaled ( 0.8, 0.8, 0.8 ) ;
197 glTranslated ( xwin, ywin, 0.0 ) ;
198 scale_factor *= 1.25 ;
210 void readConfigFile ( char *fnme )
212 FILE *fptr = fopen ( fnme, "rt" ) ;
214 char inputline [ 256 ] ;
218 /* Read a header line */
219 fgets ( inputline, 256, fptr ) ;
221 /* Read a comment line */
222 fgets ( inputline, 256, fptr ) ;
224 /* Read the window title */
225 fgets ( inputline, 256, fptr ) ;
226 /* We assume here that this line will not exceed 79 characters plus a
227 newline (window_title is 80 characters long). That'll cause a buffer
228 overflow. For a simple program like this, though, we're letting it
231 sscanf ( inputline, "%[a-zA-Z0-9!@#$%^&*()+=/\\_-\" ]", window_title ) ;
233 /* Read a comment line */
234 fgets ( inputline, 256, fptr ) ;
236 /* Read the number of affine transformations */
237 fgets ( inputline, 256, fptr ) ;
238 sscanf ( inputline, "%d", &num_trans ) ;
240 affine = (AffineTrans *)malloc ( num_trans * sizeof(AffineTrans) ) ;
242 /* Read a comment line */
243 fgets ( inputline, 256, fptr ) ;
245 for ( i = 0; i < num_trans; i++ )
247 /* Read an affine transformation definition */
248 fgets ( inputline, 256, fptr ) ;
249 sscanf ( inputline, "%lf %lf %lf %lf %lf %lf", &affine[i].a00, &affine[i].a01,
250 &affine[i].a10, &affine[i].a11, &affine[i].b0, &affine[i].b1 ) ;
253 else /* No data file, set a default */
255 printf ( "ERROR opening file <%s>\n", fnme ) ;
256 strcpy ( window_title, "Cantor Dust" ) ;
258 affine = (AffineTrans *)malloc ( num_trans * sizeof(AffineTrans) ) ;
259 affine[0].a00 = 0.25 ; affine[0].a01 = 0.00 ; affine[0].a10 = 0.00 ; affine[0].a11 = 0.25 ;
260 affine[0].b0 = 0.0 ; affine[0].b1 = 0.0 ;
261 affine[1].a00 = 0.25 ; affine[1].a01 = 0.00 ; affine[1].a10 = 0.00 ; affine[1].a11 = 0.25 ;
262 affine[1].b0 = 0.5 ; affine[1].b1 = 0.0 ;
265 for ( i = 0; i < num_trans; i++ )
267 double m00, m01, m10, m11 ; /* Matrix "I" minus "A" */
268 double determ ; /* Determinant of this matrix */
270 /* Calculate the stationary point */
272 m00 = 1.0 - affine[i].a00 ;
273 m01 = - affine[i].a01 ;
274 m10 = - affine[i].a10 ;
275 m11 = 1.0 - affine[i].a11 ;
277 determ = m00 * m11 - m01 * m10 ;
279 if ( fabs ( determ ) > 1.e-6 )
281 affine[i].statx = ( m11 * affine[i].b0 - m01 * affine[i].b1 ) / determ ;
282 affine[i].staty = ( -m10 * affine[i].b0 + m00 * affine[i].b1 ) / determ ;
285 affine[i].statx = affine[i].staty = 0.0 ;
290 main(int argc, char *argv[])
294 glutInitWindowSize(500, 250);
295 glutInitWindowPosition ( 140, 140 );
296 glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE );
297 glutInit(&argc, argv);
300 readConfigFile ( argv[1] ) ;
302 readConfigFile ( "fractals.dat" ) ;
304 fractal_window = glutCreateWindow( window_title );
306 glClearColor(1.0, 1.0, 1.0, 1.0);
308 glutReshapeFunc(Reshape);
309 glutKeyboardFunc(Key);
310 glutSpecialFunc(Special);
311 glutDisplayFunc(Display);
315 printf ( "Back from the 'freeglut' main loop\n" ) ;
317 return 0; /* ANSI C requires main to return int. */