343 lines
8.8 KiB
C
343 lines
8.8 KiB
C
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/* fractals.c */
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/*
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* Program to draw a fractal by Michael Barnsley's deterministic algorithm.
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* Algorithm:
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* (1) Define the affine transformations (of the form r(i+1) = A r(i) + b )
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* (2) Find the stationary point for each transformation
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* (3) To draw:
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* - If you are at the lowest level, draw lines connecting all the stationary points
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* - If not, call the draw function recursively with each affine transformation applied
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*/
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/*
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* User Commands:
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* +,- - increment/decrement number of levels
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* PgUp, PgDn - increase/decrease scaling
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* Arrow keys - translate viewing section
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* r - reset view
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* Escape - quit
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*/
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#include <GL/freeglut.h>
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <math.h>
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#define FGH_PI 3.14159265358979323846
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typedef struct
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{
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double a00, a01, a10, a11 ; /* Transformation matrix */
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double b0, b1 ; /* Constant vector added on */
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double statx, staty ; /* Coordinates of the stationary point */
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}
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AffineTrans ;
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/* Number of levels to draw the fractal */
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static int num_levels = 4 ;
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/* The definition of the fractal */
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static int num_trans ;
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static AffineTrans *affine ;
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/* Flag telling us to keep executing the main loop */
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static int continue_in_main_loop = 1;
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/* the window title */
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char window_title [ 80 ] ;
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/* The amount the view is translated and scaled */
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double xwin = 0.0, ywin = 0.0 ;
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double scale_factor = 1.0 ;
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static void draw_level ( int num, double m00, double m01, double m10, double m11, double n0, double n1 )
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{
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/* Draw a fractal transformed by "M", "N" as passed in */
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int i ;
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if ( num == 0 )
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{
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double x0 = m00 * affine[0].statx + m01 * affine[0].staty + n0 ;
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double y0 = m10 * affine[0].statx + m11 * affine[0].staty + n1 ;
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for ( i = 1; i < num_trans; i++ )
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{
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double x1 = m00 * affine[i].statx + m01 * affine[i].staty + n0 ;
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double y1 = m10 * affine[i].statx + m11 * affine[i].staty + n1 ;
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glVertex2d ( x0, y0 ) ;
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glVertex2d ( x1, y1 ) ;
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x0 = x1 ;
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y0 = y1 ;
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}
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}
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else
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{
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/* Map each affine transformation in the fractal through the one passed in and call "draw_level" */
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for ( i = 0; i < num_trans; i++ )
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{
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draw_level ( num-1, m00*affine[i].a00+m01*affine[i].a10, m00*affine[i].a01+m01*affine[i].a11,
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m10*affine[i].a00+m11*affine[i].a10, m10*affine[i].a01+m11*affine[i].a11,
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m00*affine[i].b0 +m01*affine[i].b1 + n0, m10*affine[i].b0 +m11*affine[i].b1 + n1 ) ;
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}
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}
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}
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static void
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Display(void)
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{
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glClear( GL_COLOR_BUFFER_BIT );
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/* the curve */
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glPushMatrix();
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glScalef(2.5, 2.5, 2.5);
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glColor4f(0.0, 0.0, 0.0, 1.0);
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glBegin ( GL_LINES ) ;
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draw_level ( num_levels, 1.0, 0.0, 0.0, 1.0, 0.0, 0.0 );
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glEnd () ;
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glPopMatrix();
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glutSwapBuffers();
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}
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static void
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Reshape(int width, int height)
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{
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float ar;
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glViewport ( 0, 0, width, height ) ;
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glMatrixMode ( GL_PROJECTION ) ;
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glLoadIdentity();
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ar = (float) width / (float) height ;
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if( ar > 1 )
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glFrustum ( -ar, ar, -1.0, 1.0, 2.0, 100.0 ) ;
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else
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glFrustum ( -1.0, 1.0, -1/ar, 1/ar, 2.0, 100.0 );
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glMatrixMode ( GL_MODELVIEW ) ;
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glLoadIdentity () ;
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xwin = -1.0 ;
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ywin = 0.0 ;
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glTranslated ( xwin, ywin, -5.0 ) ;
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}
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static void
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Key(unsigned char key, int x, int y)
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{
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int need_redisplay = 1;
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switch (key) {
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case 27: /* Escape key */
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continue_in_main_loop = 0 ;
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break;
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case '+' :
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++num_levels ;
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break ;
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case '-' :
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if ( num_levels > 0 )
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--num_levels ;
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break ;
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case 'r' : case 'R' :
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glMatrixMode ( GL_MODELVIEW ) ;
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glLoadIdentity();
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xwin = -1.0 ;
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ywin = 0.0 ;
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glTranslated ( xwin, ywin, -5.0 ) ;
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break ;
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default:
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need_redisplay = 0;
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break;
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}
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if (need_redisplay)
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glutPostRedisplay();
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}
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static void
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Special(int key, int x, int y)
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{
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int need_redisplay = 1;
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switch (key) {
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case GLUT_KEY_UP :
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glMatrixMode ( GL_MODELVIEW ) ;
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ywin += 0.1 * scale_factor ;
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glTranslated ( 0.0, 0.1 * scale_factor, 0.0 ) ;
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break ;
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case GLUT_KEY_DOWN :
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glMatrixMode ( GL_MODELVIEW ) ;
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ywin -= 0.1 * scale_factor ;
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glTranslated ( 0.0, -0.1 * scale_factor, 0.0 ) ;
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break ;
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case GLUT_KEY_LEFT :
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glMatrixMode ( GL_MODELVIEW ) ;
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xwin -= 0.1 * scale_factor ;
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glTranslated ( -0.1 * scale_factor, 0.0, 0.0 ) ;
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break ;
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case GLUT_KEY_RIGHT :
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glMatrixMode ( GL_MODELVIEW ) ;
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xwin += 0.1 * scale_factor ;
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glTranslated ( 0.1 * scale_factor, 0.0, 0.0 ) ;
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break ;
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case GLUT_KEY_PAGE_UP :
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glMatrixMode ( GL_MODELVIEW ) ;
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glTranslated ( -xwin, -ywin, 0.0 ) ;
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glScaled ( 1.25, 1.25, 1.25 ) ;
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glTranslated ( xwin, ywin, 0.0 ) ;
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scale_factor *= 0.8 ;
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break ;
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case GLUT_KEY_PAGE_DOWN :
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glMatrixMode ( GL_MODELVIEW ) ;
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glTranslated ( -xwin, -ywin, 0.0 ) ;
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glScaled ( 0.8, 0.8, 0.8 ) ;
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glTranslated ( xwin, ywin, 0.0 ) ;
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scale_factor *= 1.25 ;
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break ;
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default:
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need_redisplay = 0;
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break;
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}
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if (need_redisplay)
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glutPostRedisplay();
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}
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static void
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checkedFGets ( char *s, int size, FILE *stream )
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{
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if ( fgets ( s, size, stream ) == NULL ) {
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fprintf ( stderr, "fgets failed\n");
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exit ( EXIT_FAILURE );
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}
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}
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void readConfigFile ( char *fnme )
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{
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FILE *fptr = fopen ( fnme, "rt" ) ;
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int i ;
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char inputline [ 256 ] ;
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if ( fptr )
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{
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/* Read a header line */
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checkedFGets ( inputline, sizeof ( inputline ), fptr ) ;
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/* Read a comment line */
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checkedFGets ( inputline, sizeof ( inputline ), fptr ) ;
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/* Read the window title */
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checkedFGets ( inputline, sizeof ( inputline ), fptr ) ;
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/* We assume here that this line will not exceed 79 characters plus a
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newline (window_title is 80 characters long). That'll cause a buffer
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overflow. For a simple program like this, though, we're letting it
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slide!
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*/
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sscanf ( inputline, "%[a-zA-Z0-9!@#$%^&*()+=/\\_-\" ]", window_title ) ;
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/* Read a comment line */
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checkedFGets ( inputline, sizeof ( inputline ), fptr ) ;
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/* Read the number of affine transformations */
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checkedFGets ( inputline, sizeof ( inputline ), fptr ) ;
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sscanf ( inputline, "%d", &num_trans ) ;
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affine = (AffineTrans *)malloc ( num_trans * sizeof(AffineTrans) ) ;
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/* Read a comment line */
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checkedFGets ( inputline, sizeof ( inputline ), fptr ) ;
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for ( i = 0; i < num_trans; i++ )
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{
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/* Read an affine transformation definition */
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checkedFGets ( inputline, sizeof ( inputline ), fptr ) ;
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sscanf ( inputline, "%lf %lf %lf %lf %lf %lf", &affine[i].a00, &affine[i].a01,
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&affine[i].a10, &affine[i].a11, &affine[i].b0, &affine[i].b1 ) ;
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}
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}
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else /* No data file, set a default */
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{
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printf ( "ERROR opening file <%s>\n", fnme ) ;
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strcpy ( window_title, "Koch Snowflake" ) ;
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num_trans = 4 ;
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affine = (AffineTrans *)malloc ( num_trans * sizeof(AffineTrans) ) ;
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affine[0].a00 = 1/3. ; affine[0].a01 = 0.00 ; affine[0].a10 = 0.00 ; affine[0].a11 = 1/3. ;
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affine[0].b0 = 0.0 ; affine[0].b1 = 0.0 ;
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affine[1].a00 = 1/6. ; affine[1].a01 = -1/3.*sin(FGH_PI/3.) ; affine[1].a10 = 1/3.*sin(FGH_PI/3.) ; affine[1].a11 = 1/6. ;
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affine[1].b0 = 1/3. ; affine[1].b1 = 0.0 ;
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affine[2].a00 = 1/6. ; affine[2].a01 = -1/3.*sin(-FGH_PI/3.) ; affine[2].a10 = 1/3.*sin(-FGH_PI/3.) ; affine[2].a11 = 1/6. ;
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affine[2].b0 = 0.5 ; affine[2].b1 = sqrt(3)/6. ;
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affine[3].a00 = 1/3. ; affine[3].a01 = 0.00 ; affine[3].a10 = 0.00 ; affine[3].a11 = 1/3. ;
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affine[3].b0 = 2/3. ; affine[3].b1 = 0.0 ;
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}
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for ( i = 0; i < num_trans; i++ )
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{
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double m00, m01, m10, m11 ; /* Matrix "I" minus "A" */
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double determ ; /* Determinant of this matrix */
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/* Calculate the stationary point */
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m00 = 1.0 - affine[i].a00 ;
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m01 = - affine[i].a01 ;
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m10 = - affine[i].a10 ;
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m11 = 1.0 - affine[i].a11 ;
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determ = m00 * m11 - m01 * m10 ;
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if ( fabs ( determ ) > 1.e-6 )
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{
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affine[i].statx = ( m11 * affine[i].b0 - m01 * affine[i].b1 ) / determ ;
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affine[i].staty = ( -m10 * affine[i].b0 + m00 * affine[i].b1 ) / determ ;
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}
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else
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affine[i].statx = affine[i].staty = 0.0 ;
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}
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}
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int
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main(int argc, char *argv[])
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{
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glutInitWindowSize(500, 250);
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glutInitWindowPosition ( 140, 140 );
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glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE );
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glutInit(&argc, argv);
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if ( argc > 1 )
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readConfigFile ( argv[1] ) ;
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else
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readConfigFile ( "fractals.dat" ) ;
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glutCreateWindow( window_title );
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glClearColor(1.0, 1.0, 1.0, 1.0);
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glutReshapeFunc(Reshape);
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glutKeyboardFunc(Key);
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glutSpecialFunc(Special);
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glutDisplayFunc(Display);
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#ifdef WIN32
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#endif
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while ( continue_in_main_loop )
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glutMainLoopEvent();
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printf ( "Back from the 'freeglut' main loop\n" ) ;
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return 0; /* ANSI C requires main to return int. */
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}
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