--- /dev/null
+/*
+ * Lorenz Strange Attractor
+ *
+ * Written by John F. Fay in honor of the "freeglut" 2.0.0 release in July 2003
+ *
+ * What it does:
+ * This program starts with two particles right next to each other. The particles
+ * move through a three-dimensional phase space governed by the following equations:
+ * dx/dt = sigma * ( y - x )
+ * dy/dt = r * x - y + x * z
+ * dz/dt = x * y + b * z
+ * These are the Lorenz equations and define the "Lorenz Attractor." Any two particles
+ * arbitrarily close together will move apart as time increases, but their tracks are
+ * confined within a region of the space.
+ *
+ * Commands:
+ * Arrow keys: Rotate the view
+ * PgUp, PgDn: Zoom in and out
+ * Mouse click: Center on the nearest point on a particle trajectory
+ *
+ * 'r'/'R': Reset the simulation
+ * 'm'/'M': Modify the Lorenz parameters (in the text window)
+ * 's'/'S': Stop (the advancement in time)
+ * 'g'/'G': Go
+ * <spacebar>: Single-step
+ * <Escape>: Quit
+ */
+
+/* Include Files */
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <math.h>
+#include <time.h>
+#include <GL/freeglut.h>
+
+
+/************************************** Defined Constants ***************************************/
+/* Number of points to draw in the curves */
+#define NUM_POINTS 512
+
+/* Angle to rotate when the user presses an arrow key */
+#define ROTATION_ANGLE 5.0
+
+/* Amount to scale bu when the user presses PgUp or PgDn */
+#define SCALE_FACTOR 0.8
+
+
+/*************************************** Global Variables ***************************************/
+/* Lorenz Attractor variables */
+double s0 = 10.0, r0 = 28.0, b0 = 8.0/3.0 ; /* Default Lorenz attactor parameters */
+double time_step = 0.03 ; /* Time step in the simulation */
+double sigma = 10.0, r = 28.0, b = 8.0/3.0 ; /* Lorenz attactor parameters */
+double red_position[NUM_POINTS][3] ; /* Path of the red point */
+double grn_position[NUM_POINTS][3] ; /* Path of the green point */
+int array_index ; /* Position in *_position arrays of most recent point */
+double distance = 0.0 ; /* Distance between the two points */
+
+/* GLUT variables */
+double yaw = 0.0, pit = 0.0 ; /* Euler angles of the viewing rotation */
+double scale = 1.0 ; /* Scale factor */
+double xcen = 0.0, ycen = 0.0, zcen = 0.0 ; /* Coordinates of the point looked at */
+
+int animate = 1 ; /* 0 - stop, 1 = go, 2 = single-step */
+
+
+/******************************************* Functions ******************************************/
+
+/* The Lorenz Attractor */
+void calc_deriv ( double position[3], double deriv[3] )
+{
+ /* Calculate the Lorenz attractor derivatives */
+ deriv[0] = sigma * ( position[1] - position[0] ) ;
+ deriv[1] = ( r + position[2] ) * position[0] - position[1] ;
+ deriv[2] = -position[0] * position[1] - b * position[2] ;
+}
+
+void advance_in_time ( double time_step, double position[3], double new_position[3] )
+{
+ /* Move a point along the Lorenz attractor */
+ double deriv0[3], deriv1[3], deriv2[3], deriv3[3] ;
+ int i ;
+ memcpy ( new_position, position, 3 * sizeof(double) ) ; /* Save the present values */
+
+ /* First pass in a Fourth-Order Runge-Kutta integration method */
+ calc_deriv ( position, deriv0 ) ;
+ for ( i = 0; i < 3; i++ )
+ new_position[i] = position[i] + 0.5 * time_step * deriv0[i] ;
+
+ /* Second pass */
+ calc_deriv ( new_position, deriv1 ) ;
+ for ( i = 0; i < 3; i++ )
+ new_position[i] = position[i] + 0.5 * time_step * deriv1[i] ;
+
+ /* Third pass */
+ calc_deriv ( position, deriv2 ) ;
+ for ( i = 0; i < 3; i++ )
+ new_position[i] = position[i] + time_step * deriv2[i] ;
+
+ /* Second pass */
+ calc_deriv ( new_position, deriv3 ) ;
+ for ( i = 0; i < 3; i++ )
+ new_position[i] = position[i] + 0.1666666666666666667 * time_step *
+ ( deriv0[i] + 2.0 * ( deriv1[i] + deriv2[i] ) + deriv3[i] ) ;
+}
+
+/* GLUT callbacks */
+
+void key_cb ( unsigned char key, int x, int y )
+{
+ int i ;
+ char inputline [ 80 ] ;
+
+ switch ( key )
+ {
+ case 'r' : case 'R' : /* Reset the simulation */
+ /* Reset the Lorenz parameters */
+ sigma = s0 ;
+ b = b0 ;
+ r = r0 ;
+ /* Set an initial position */
+ red_position[0][0] = (double)rand() / (double)RAND_MAX ;
+ red_position[0][1] = (double)rand() / (double)RAND_MAX ;
+ red_position[0][2] = (double)rand() / (double)RAND_MAX ;
+ grn_position[0][0] = (double)rand() / (double)RAND_MAX ;
+ grn_position[0][1] = (double)rand() / (double)RAND_MAX ;
+ grn_position[0][2] = (double)rand() / (double)RAND_MAX ;
+ array_index = 0 ;
+ /* Initialize the arrays */
+ for ( i = 1; i < NUM_POINTS; i++ )
+ {
+ memcpy ( red_position[i], red_position[0], 3 * sizeof(double) ) ;
+ memcpy ( grn_position[i], grn_position[0], 3 * sizeof(double) ) ;
+ }
+
+ break ;
+
+ case 'm' : case 'M' : /* Modify the Lorenz parameters */
+ printf ( "Please enter new value for <sigma> (default %lf, currently %lf): ", s0, sigma ) ;
+ fgets ( inputline, 79, stdin ) ;
+ sscanf ( inputline, "%lf", &sigma ) ;
+
+ printf ( "Please enter new value for <b> (default %lf, currently %lf): ", b0, b ) ;
+ fgets ( inputline, 79, stdin ) ;
+ sscanf ( inputline, "%lf", &b ) ;
+
+ printf ( "Please enter new value for <r> (default %lf, currently %lf): ", r0, r ) ;
+ fgets ( inputline, 79, stdin ) ;
+ sscanf ( inputline, "%lf", &r ) ;
+
+ break ;
+
+ case 's' : case 'S' : /* Stop the animation */
+ animate = 0 ;
+ break ;
+
+ case 'g' : case 'G' : /* Start the animation */
+ animate = 1 ;
+ break ;
+
+ case ' ' : /* Spacebar: Single step */
+ animate = 2 ;
+ break ;
+
+ case 27 : /* Escape key */
+ glutLeaveMainLoop () ;
+ break ;
+ }
+}
+
+void special_cb ( int key, int x, int y )
+{
+ switch ( key )
+ {
+ case GLUT_KEY_UP : /* Rotate up a little */
+ glRotated ( ROTATION_ANGLE, 0.0, 1.0, 0.0 ) ;
+ break ;
+
+ case GLUT_KEY_DOWN : /* Rotate down a little */
+ glRotated ( -ROTATION_ANGLE, 0.0, 1.0, 0.0 ) ;
+ break ;
+
+ case GLUT_KEY_LEFT : /* Rotate left a little */
+ glRotated ( ROTATION_ANGLE, 0.0, 0.0, 1.0 ) ;
+ break ;
+
+ case GLUT_KEY_RIGHT : /* Rotate right a little */
+ glRotated ( -ROTATION_ANGLE, 0.0, 0.0, 1.0 ) ;
+ break ;
+
+ case GLUT_KEY_PAGE_UP : /* Zoom in a little */
+ glScaled ( 1.0 / SCALE_FACTOR, 1.0 / SCALE_FACTOR, 1.0 / SCALE_FACTOR ) ;
+ break ;
+
+ case GLUT_KEY_PAGE_DOWN : /* Zoom out a little */
+ glScaled ( SCALE_FACTOR, SCALE_FACTOR, SCALE_FACTOR ) ;
+ break ;
+ }
+
+ glutPostRedisplay () ;
+}
+
+void mouse_cb ( int button, int updown, int x, int y )
+{
+ if ( updown == GLUT_DOWN )
+ {
+ double dist = 1.0e20 ; /* A very large number */
+ (void) dist; /* what's this all about? */
+ }
+}
+
+void draw_curve ( int index, double position [ NUM_POINTS ][3] )
+{
+ int i = index ;
+
+ glBegin ( GL_LINE_STRIP ) ;
+ do
+ {
+ i = ( i == NUM_POINTS-1 ) ? 0 : i + 1 ;
+ glVertex3dv ( position[i] ) ;
+ }
+ while ( i != index ) ;
+
+ glEnd () ;
+}
+
+void display_cb ( void )
+{
+ char string [ 80 ] ;
+
+ glClear ( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ) ;
+
+ glColor3d ( 1.0, 1.0, 1.0 ) ; /* White */
+ /* Draw some axes */
+ glBegin ( GL_LINES ) ;
+ glVertex3d ( 0.0, 0.0, 0.0 ) ;
+ glVertex3d ( 2.0, 0.0, 0.0 ) ;
+ glVertex3d ( 0.0, 0.0, 0.0 ) ;
+ glVertex3d ( 0.0, 1.0, 0.0 ) ;
+ glVertex3d ( 0.0, 0.0, 0.0 ) ;
+ glVertex3d ( 0.0, 0.0, 1.0 ) ;
+ glEnd () ;
+
+ glColor3d ( 1.0, 0.0, 0.0 ) ; /* Red */
+ draw_curve ( array_index, red_position ) ;
+
+ glColor3d ( 0.0, 1.0, 0.0 ) ; /* Green */
+ draw_curve ( array_index, grn_position ) ;
+
+ /* Print the distance between the two points */
+ glColor3d ( 1.0, 1.0, 1.0 ) ; /* White */
+ sprintf ( string, "Distance: %10.6lf", distance ) ;
+ glRasterPos2i ( 10, 10 ) ;
+ glutBitmapString ( GLUT_BITMAP_HELVETICA_12, string ) ;
+
+ glutSwapBuffers();
+}
+
+void reshape_cb ( 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, 10.0, 100.0 ) ;
+ glMatrixMode ( GL_MODELVIEW ) ;
+ glLoadIdentity () ;
+ xcen = 0.0 ;
+ ycen = 0.0 ;
+ zcen = 0.0 ;
+ glTranslated ( xcen, ycen, zcen - 50.0 ) ;
+}
+
+
+void timer_cb ( int value )
+{
+ /* Function called at regular intervals to update the positions of the points */
+ double deltax, deltay, deltaz ;
+ int new_index = array_index + 1 ;
+
+ /* Set the next timed callback */
+ glutTimerFunc ( 30, timer_cb, 0 ) ;
+
+ if ( animate > 0 )
+ {
+ if ( new_index == NUM_POINTS ) new_index = 0 ;
+ advance_in_time ( time_step, red_position[array_index], red_position[new_index] ) ;
+ advance_in_time ( time_step, grn_position[array_index], grn_position[new_index] ) ;
+ array_index = new_index ;
+
+ deltax = red_position[array_index][0] - grn_position[array_index][0] ;
+ deltay = red_position[array_index][1] - grn_position[array_index][1] ;
+ deltaz = red_position[array_index][2] - grn_position[array_index][2] ;
+ distance = sqrt ( deltax * deltax + deltay * deltay + deltaz * deltaz ) ;
+
+ if ( animate == 2 ) animate = 0 ;
+ }
+
+ glutPostRedisplay () ;
+}
+
+
+
+/* The Main Program */
+
+int main ( int argc, char *argv[] )
+{
+ int pargc = argc ;
+
+ /* Initialize the random number generator */
+ srand ( 1023 ) ;
+
+ /* Set up the OpenGL parameters */
+ /* glDrawBuffer ( GL_BACK ) ;*/
+ glEnable ( GL_DEPTH_TEST ) ;
+ glClearColor ( 0.0, 0.0, 0.0, 0.0 ) ;
+ glClearDepth ( 1.0 ) ;
+
+ /* Initialize GLUT */
+ glutInitWindowSize ( 600, 600 ) ;
+ glutInit ( &pargc, argv ) ;
+ glutInitDisplayMode ( GLUT_RGB | GLUT_DOUBLE | GLUT_DEPTH ) ;
+
+ /* Create the window */
+ glutCreateWindow ( "Lorenz Attractor" ) ;
+ glutKeyboardFunc ( key_cb ) ;
+ glutMouseFunc ( mouse_cb ) ;
+ glutSpecialFunc ( special_cb ) ;
+ glutDisplayFunc ( display_cb ) ;
+ glutReshapeFunc ( reshape_cb ) ;
+ glutTimerFunc ( 30, timer_cb, 0 ) ;
+
+ /* Initialize the attractor: The easiest way is to call the keyboard callback with an
+ * argument of 'r' for Reset.
+ */
+ key_cb ( 'r', 0, 0 ) ;
+
+ /* Enter the GLUT main loop */
+ glutMainLoop () ;
+
+ return 0;
+}
+
projects / freeglut / blobdiff