)- If you are at the lowest level, draw lines connecting all the stationary points
- If not, call the draw function recursively with each affine transformation applied
Algorithm:
)User Interaction:
OpenGLUT Fractal Demonstration
#include <GL/openglut.h> #include <math.h> #include <stdio.h> #include <stdlib.h> #include <string.h> typedef struct { double a00, a01, a10, a11; /* Transformation matrix */ double b0, b1; /* Constant vector added on */ double statx, staty; /* Coordinates of the stationary point */ } AffineTrans; /* Number of levels to draw the fractal */ static int num_levels = 0; /* The definition of the fractal */ static int num_trans; static AffineTrans *affine; /* the window title */ #define WIN_TITLE_LENGTH 80 char window_title[ WIN_TITLE_LENGTH + 1 ]; /* The amount the view is translated and scaled */ double xwin = 0.0, ywin = 0.0; double scale_factor = 1.0; static void draw_level( int num, double m00, double m01, double m10, double m11, double n0, double n1 ) { /* Draw a fractal transformed by "M", "N" as passed in */ int i; if( !num ) { double x0 = m00 * affine[0].statx + m01 * affine[0].staty + n0; double y0 = m10 * affine[0].statx + m11 * affine[0].staty + n1; for( i = 1; i < num_trans; i++ ) { double x1 = m00 * affine[i].statx + m01 * affine[i].staty + n0; double y1 = m10 * affine[i].statx + m11 * affine[i].staty + n1; glVertex2d ( x0, y0 ); glVertex2d ( x1, y1 ); x0 = x1; y0 = y1; } } else /* * Map each affine transformation in the fractal through * the one passed in and call draw_level() */ for( i = 0; i < num_trans; i++ ) draw_level( num-1, m00*affine[i].a00+m01*affine[i].a10, m00*affine[i].a01+m01*affine[i].a11, m10*affine[i].a00+m11*affine[i].a10, m10*affine[i].a01+m11*affine[i].a11, m00*affine[i].b0 +m01*affine[i].b1 + n0, m10*affine[i].b0 +m11*affine[i].b1 + n1 ); } static void Display( void ) { glClear( GL_COLOR_BUFFER_BIT ); /* the curve */ glPushMatrix(); glScalef(2.5, 2.5, 2.5); glColor4f(0.0, 0.0, 0.0, 1.0); glBegin( GL_LINES ); draw_level( num_levels, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0 ); glEnd( ); glPopMatrix(); glutSwapBuffers(); } static void Reshape( int width, int height ) { float ar; glViewport( 0, 0, width, height ); glMatrixMode( GL_PROJECTION ); glLoadIdentity( ); ar = ( float )width / ( float )height; if( ar > 1 ) glFrustum( -ar, ar, -1.0, 1.0, 2.0, 100.0 ); else glFrustum( -1.0, 1.0, -1/ar, 1/ar, 2.0, 100.0 ); glMatrixMode( GL_MODELVIEW ); glLoadIdentity( ); xwin = -1.0; ywin = 0.0; glTranslated( xwin, ywin, -5.0 ); } static void Key( unsigned char key, int x, int y ) { int need_redisplay = 1; switch (key) { case 27: /* Escape key */ glutLeaveMainLoop (); break; case '+' : ++num_levels; break; case '-' : if ( num_levels > 0 ) --num_levels; break; case 'r' : case 'R' : glMatrixMode ( GL_MODELVIEW ); glLoadIdentity(); xwin = -1.0; ywin = 0.0; glTranslated ( xwin, ywin, -5.0 ); break; default: need_redisplay = 0; break; } if (need_redisplay) glutPostRedisplay(); } static void Special( int key, int x, int y ) { int need_redisplay = 1; switch (key) { case GLUT_KEY_UP : glMatrixMode ( GL_MODELVIEW ); ywin += 0.1 * scale_factor; glTranslated ( 0.0, 0.1 * scale_factor, 0.0 ); break; case GLUT_KEY_DOWN : glMatrixMode ( GL_MODELVIEW ); ywin -= 0.1 * scale_factor; glTranslated ( 0.0, -0.1 * scale_factor, 0.0 ); break; case GLUT_KEY_LEFT : glMatrixMode ( GL_MODELVIEW ); xwin -= 0.1 * scale_factor; glTranslated ( -0.1 * scale_factor, 0.0, 0.0 ); break; case GLUT_KEY_RIGHT : glMatrixMode ( GL_MODELVIEW ); xwin += 0.1 * scale_factor; glTranslated ( 0.1 * scale_factor, 0.0, 0.0 ); break; case GLUT_KEY_PAGE_UP : glMatrixMode ( GL_MODELVIEW ); glTranslated ( -xwin, -ywin, 0.0 ); glScaled ( 1.25, 1.25, 1.25 ); glTranslated ( xwin, ywin, 0.0 ); scale_factor *= 0.8; break; case GLUT_KEY_PAGE_DOWN : glMatrixMode ( GL_MODELVIEW ); glTranslated ( -xwin, -ywin, 0.0 ); glScaled ( 0.8, 0.8, 0.8 ); glTranslated ( xwin, ywin, 0.0 ); scale_factor *= 1.25; break; default: need_redisplay = 0; break; } if (need_redisplay) glutPostRedisplay(); } void readConfigFile ( char *fnme ) { FILE *fptr = fopen ( fnme, "rt" ); int i; char inputline [ 256 ]; if ( fptr ) { /* Read a header line */ fgets( inputline, 256, fptr ); /* Read a comment line */ fgets( inputline, 256, fptr ); /* Read the window title */ fgets( inputline, 256, fptr ); /* We assume here that this line will not exceed 79 characters plus a newline (window_title is 80 characters long). That'll cause a buffer overflow. For a simple program like this, though, we're letting it slide! */ sscanf( inputline, "%[a-zA-Z0-9!@#$%^&*()+=/\\_-\" ]", window_title ); /* Read a comment line */ fgets( inputline, 256, fptr ); /* Read the number of affine transformations */ fgets( inputline, 256, fptr ); sscanf( inputline, "%d", &num_trans ); affine = (AffineTrans *)malloc ( num_trans * sizeof(AffineTrans) ); /* Read a comment line */ fgets( inputline, 256, fptr ); for ( i = 0; i < num_trans; i++ ) { /* Read an affine transformation definition */ fgets( inputline, 256, fptr ); sscanf( inputline, "%lf %lf %lf %lf %lf %lf", &affine[i].a00, &affine[i].a01, &affine[i].a10, &affine[i].a11, &affine[i].b0, &affine[i].b1 ); } } else /* No data file, set a default */ { printf( "ERROR opening file <%s>\n", fnme ); strncpy( window_title, "Cantor Dust", WIN_TITLE_LENGTH ); num_trans = 2; affine = (AffineTrans *)malloc ( num_trans * sizeof(AffineTrans) ); affine[0].a00 = 0.25; affine[0].a01 = 0.00; affine[0].a10 = 0.00; affine[0].a11 = 0.25; affine[0].b0 = 0.0; affine[0].b1 = 0.0; affine[1].a00 = 0.25; affine[1].a01 = 0.00; affine[1].a10 = 0.00; affine[1].a11 = 0.25; affine[1].b0 = 0.5; affine[1].b1 = 0.0; } for ( i = 0; i < num_trans; i++ ) { double m00, m01, m10, m11; /* Matrix "I" minus "A" */ double determ; /* Determinant of this matrix */ /* Calculate the stationary point */ m00 = 1.0 - affine[i].a00; m01 = - affine[i].a01; m10 = - affine[i].a10; m11 = 1.0 - affine[i].a11; determ = m00 * m11 - m01 * m10; if ( fabs ( determ ) > 1.e-6 ) { affine[i].statx = ( m11 * affine[i].b0 - m01 * affine[i].b1 ) / determ; affine[i].staty = ( -m10 * affine[i].b0 + m00 * affine[i].b1 ) / determ; } else affine[i].statx = affine[i].staty = 0.0; } } int main(int argc, char *argv[]) { int fractal_window; glutInitWindowSize(500, 250); glutInitWindowPosition ( 140, 140 ); glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE ); glutInit(&argc, argv); if ( argc > 1 ) readConfigFile ( argv[1] ); else readConfigFile ( "fractals.dat" ); fractal_window = glutCreateWindow( window_title ); glClearColor( 1.0, 1.0, 1.0, 1.0 ); glutReshapeFunc( Reshape ); glutKeyboardFunc( Key ); glutSpecialFunc( Special ); glutDisplayFunc( Display ); glutMainLoop( ); printf( "Back from the 'freeglut' main loop\n" ); return EXIT_SUCCESS; }