)- 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
Program to draw a fractal by Michael Barnsley's deterministic algorithm.
Algorithm:
)User Interaction:
OpenGLUT Fractal Demonstration
#include <GL/openglut.h> #include <math.h> #include <stdio.h> #include <stdlib.h> #include <string.h> #ifdef MSC_VER #include <crtdbg.h> // DUMP MEMORY LEAKS #endif 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 */ double xwin = 0.0, ywin = 0.0; double scale_factor = 1.0; /* The current point */ double current_x = 0.0, current_y = 0.0; /* Signals when a glClear is needed */ static GLboolean needClear = GL_TRUE; 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; for( i = 0; i < 10; i++ ) { int random = ( rand( ) >> 10 ) % num_trans; double new_x = affine[random].a00 * current_x + affine[random].a01 * current_y + affine[random].b0; double new_y = affine[random].a10 * current_x + affine[random].a11 * current_y + affine[random].b1; glVertex2d ( new_x, new_y ); current_x = new_x; current_y = new_y; } } static void Display( void ) { if( needClear ) { glClear( GL_COLOR_BUFFER_BIT ); needClear = GL_FALSE; } /* the curve */ glPushMatrix( ); glScaled( 2.5, 2.5, 2.5 ); glColor4f( 0.0, 0.0, 0.0, 1.0 ); glBegin( GL_POINTS ); draw_level( num_levels, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0 ); glEnd( ); glPopMatrix( ); glFlush( ); glutPostRedisplay( ); /* Keep calling this function. */ } 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); needClear = GL_TRUE; } static void Key(unsigned char key, int x, int y) { int changed_settings = 1; switch (key) { case 27: /* Escape key */ glutLeaveMainLoop (); break; case 'r' : case 'R' : glMatrixMode(GL_MODELVIEW); glLoadIdentity(); xwin = -1.0; ywin = 0.0; glTranslated(xwin, ywin, -5.0); break; default: changed_settings = 0; break; } if (changed_settings) needClear = GL_TRUE; glutPostRedisplay(); } static void Special( int key, int x, int y ) { int changed_settings = 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: changed_settings = 0; break; } if (changed_settings) needClear = GL_TRUE; glutPostRedisplay(); } static int mouse_x = 0, mouse_y = 0; static int button_down = GLUT_DOWN; static void Mouse ( int button, int updown, int x, int y ) { button_down = updown; if ( updown == GLUT_DOWN ) { mouse_x = x; mouse_y = y; } } static void MouseMotion ( int x, int y ) { int window_width = glutGet ( GLUT_WINDOW_WIDTH ); int window_height = glutGet ( GLUT_WINDOW_HEIGHT ); int window_size = ( window_width < window_height ) ? window_width : window_height; double delta_x = 5.0 * (double)(x - mouse_x) / (double)(window_size); double delta_y = 5.0 * (double)(y - mouse_y) / (double)(window_size); xwin += delta_x * scale_factor; ywin -= delta_y * scale_factor; glMatrixMode ( GL_MODELVIEW ); glTranslated ( delta_x * scale_factor, -delta_y * scale_factor, 0.0 ); needClear = GL_TRUE; glutPostRedisplay(); mouse_x = x; mouse_y = y; } static void MouseWheel( int wheel_number, int direction, int x, int y ) { double scale = ( direction > 0 ) ? 1.25 : 0.8; glMatrixMode ( GL_MODELVIEW ); glTranslated ( -xwin, -ywin, 0.0 ); glScaled ( scale, scale, scale ); glTranslated ( xwin, ywin, 0.0 ); scale_factor /= scale; needClear = GL_TRUE; 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; glutInitDisplayMode( GLUT_RGB | GLUT_SINGLE ); glutInitWindowSize(500, 250); glutInitWindowPosition ( 140, 140 ); 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 ); glutMouseFunc( Mouse ); glutMotionFunc( MouseMotion ); glutMouseWheelFunc( MouseWheel ); glutMainLoop( ); free( affine ); #ifdef MSC_VER _CrtDumpMemoryLeaks( ); /* DUMP MEMORY LEAK INFORMATION */ #endif return EXIT_SUCCESS; }