OpenGLUT 0.6.3 development - OpenGLUT: fractals.c File Reference
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# fractals.c File Reference

## Detailed Description

Program to draw a fractal by Michael Barnsley's deterministic algorithm.

Algorithm:

- Define the affine transformations (of the form )
- Find the stationary point for each transformation
- 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 Interaction:

- +,- : increment/decrement number of levels
- PgUp, PgDn : increase/decrease scaling
- Arrow keys : translate viewing section
- r : reset view
- Escape : quit

Author:
  Portions Copyright (C) 2004, the OpenGLUT project contributors.
  OpenGLUT branched from freeglut in February, 2004.

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;
    }

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