+/* fractals.c */
+/*
+ * Program to draw a fractal by Michael Barnsley's deterministic algorithm.
+ * Algorithm:
+ * (1) Define the affine transformations (of the form r(i+1) = A r(i) + b )
+ * (2) Find the stationary point for each transformation
+ * (3) To draw:
+ * - 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
+ */
+
+/*
+ * User Commands:
+ * +,- - increment/decrement number of levels
+ * PgUp, PgDn - increase/decrease scaling
+ * Arrow keys - translate viewing section
+ * r - reset view
+ * Escape - quit
+ */
+
+#include <GL/freeglut.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.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 */
+char window_title [ 80 ] ;
+
+/* The amount the view is translated and scaled */
+float xwin = 0.0, ywin = 0.0 ;
+float 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 == 0 )
+ {
+ 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 ;
+
+ glVertex2f ( x0, y0 ) ;
+ glVertex2f ( 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 | GL_DEPTH_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;
+ glFrustum(-ar, ar, -1.0, 1.0, 2.0, 100.0);
+ glMatrixMode(GL_MODELVIEW);
+ glLoadIdentity();
+ xwin = -1.0 ;
+ ywin = 0.0 ;
+ glTranslatef(xwin, ywin, -5.0);
+}
+
+static void
+Key(unsigned char key, int x, int y)
+{
+ 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 ;
+ glTranslatef(xwin, ywin, -5.0);
+
+ break ;
+ }
+
+ glutPostRedisplay();
+}
+
+static void
+Special(int key, int x, int y)
+{
+ switch (key) {
+ case GLUT_KEY_UP :
+ glMatrixMode(GL_MODELVIEW);
+ ywin += 0.1 * scale_factor ;
+ glTranslatef(0.0, 0.1 * scale_factor, 0.0);
+ break ;
+
+ case GLUT_KEY_DOWN :
+ glMatrixMode(GL_MODELVIEW);
+ ywin -= 0.1 * scale_factor ;
+ glTranslatef(0.0, -0.1 * scale_factor, 0.0);
+ break ;
+
+ case GLUT_KEY_LEFT :
+ glMatrixMode(GL_MODELVIEW);
+ xwin -= 0.1 * scale_factor ;
+ glTranslatef(-0.1 * scale_factor, 0.0, 0.0);
+ break ;
+
+ case GLUT_KEY_RIGHT :
+ glMatrixMode(GL_MODELVIEW);
+ xwin += 0.1 * scale_factor ;
+ glTranslatef(0.1 * scale_factor, 0.0, 0.0);
+ break ;
+
+ case GLUT_KEY_PAGE_UP :
+ glMatrixMode(GL_MODELVIEW);
+ glTranslatef ( -xwin, -ywin, 0.0 ) ;
+ glScalef(1.25, 1.25, 1.25);
+ glTranslatef ( xwin, ywin, 0.0 ) ;
+ scale_factor *= 0.8 ;
+ break ;
+
+ case GLUT_KEY_PAGE_DOWN :
+ glMatrixMode(GL_MODELVIEW);
+ glTranslatef ( -xwin, -ywin, 0.0 ) ;
+ glScalef(0.8, 0.8, 0.8);
+ glTranslatef ( xwin, ywin, 0.0 ) ;
+ scale_factor *= 1.25 ;
+ break ;
+ }
+
+ glutPostRedisplay();
+}
+
+void readConfigFile ( char *fnme )
+{
+ FILE *fptr = fopen ( fnme, "rt" ) ;
+ int i ;
+ char inputline [ 256 ] ;
+
+ /* Read a header line */
+ fgets ( inputline, 256, fptr ) ;
+
+ /* Read a comment line */
+ fgets ( inputline, 256, fptr ) ;
+
+ /* Read the window title */
+ fgets ( inputline, 256, fptr ) ;
+ sscanf ( inputline, "%s", 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++ )
+ {
+ double m00, m01, m10, m11 ; /* Matrix "I" minus "A" */
+ double determ ; /* Determinant of this matrix */
+
+ /* 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 ) ;
+
+ /* 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 ;
+
+ if ( argc > 1 )
+ readConfigFile ( argv[1] ) ;
+ else
+ readConfigFile ( "fractals.dat" ) ;
+
+ glutInit(&argc, argv);
+ glutInitWindowSize(500, 250);
+ glutInitWindowPosition ( 140, 140 ) ;
+
+ glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH);
+
+ 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 0; /* ANSI C requires main to return int. */
+}