#include <stdio.h>
#include <stdlib.h>
#include <stdarg.h>
#define GL_GLEXT_PROTOTYPES
#ifdef __APPLE__
#include <GLUT/glut.h>
#else
#include <GL/glut.h>
#endif
/* Lorenz Parameters */
double s = 10;
double b = 2.6666;
double r = 28;
// Globals
int th=0; // Azimuth of view angle
int ph=0; // Elevation of view angle
double w=0.02; // W variable
double dim=2; // Dimension of orthogonal box
char* text[] = {"3D"}; // Dimension display text
double dt = 0.001;
double dz = 0;
double dw = 1;
double l[60000][4];
int i = 0;
char set = 's';
#define LEN 8192 // Maximum length of text string
void Print(const char* format , ...)
{
char buf[LEN];
char* ch=buf;
va_list args;
// Turn the parameters into a character string
va_start(args,format);
vsnprintf(buf,LEN,format,args);
va_end(args);
// Display the characters one at a time at the current raster position
while (*ch)
glutBitmapCharacter(GLUT_BITMAP_HELVETICA_18,*ch++);
}
void loAt(void)
{
double x = 1;
double y = 1;
double z = 1;
double dx = 0;
double dy = 0;
double dz = 0;
int i = 0;
/* Time step */
double dt = 0.001;
for (i = 0; i<60000; i++)
{
dx = s*(y-x);
dy = x*(r-z)-y;
dz = x*y - b*z;
x += dt*dx;
y += dt*dy;
z += dt*dz;
l[i][0] = x*w;
l[i][1] = y*w;
l[i][2] = z*w;
}
}
void display()
{
loAt();
glClear(GL_COLOR_BUFFER_BIT);
// Reset previous transforms
glLoadIdentity();
// Set view angle
glRotated(ph,1,0,0);
glRotated(th,0,1,0);
int i;
glBegin(GL_LINE_STRIP);
for (i=0;i<60000;i++)
{
glColor3dv(l[i]);
glVertex3dv(l[i]);
}
glEnd();
// Draw axes in white
glColor3f(1,0,0);
glBegin(GL_LINES);
glVertex3d(0,0,0);
glVertex3d(1,0,0);
glVertex3d(0,0,0);
glVertex3d(0,1,0);
glVertex3d(0,0,0);
glVertex3d(0,0,1);
glEnd();
// Label axes
glRasterPos3d(1,0,0);
Print("X");
glRasterPos3d(0,1,0);
Print("Y");
glRasterPos3d(0,0,1);
Print("Z");
// Display parameters
glWindowPos2i(5,5);
Print("View Angle=%d,%d",th,ph);
// Flush and swap
glFlush();
glutSwapBuffers();
}
void key(unsigned char ch,int x,int y)
{
// Exit on ESC
if (ch == 27)
exit(0);
// Reset view angle
else if (ch == '0')
{
th = ph = 0;
dw = 1;
dz = 0;
dim = 55;
}
else if (ch=='a')
s -= 1; // decrease sigma
else if (ch=='q')
s += 1; // increase sigma
else if (ch=='s')
b -= 0.5; // decrease beta
else if (ch=='w')
b += 0.5; // increase beta
else if (ch=='d')
r -= 1; // decrease rho
else if (ch=='e')
r += 1; // increase rho
// Switch dimensions
// Switch formula variable to adjust
// Increase variable for lorenz equation
else if (ch == '+')
{
if (set == 's')
{
s = s + 0.5;
}
else if (set == 'b')
{
b = b + 0.2;
}
else if (set == 'r')
{
r = r + 1;
}
else if (set == 'w')
{
dw = dw + 1;
}
else if (set == 'z')
{
dz = dz + 1;
}
else if (set == 'd')
{
dim = dim + 5;
}
}
// Decrease variable for lorenz equation
else if (ch == '-')
{
if (set == 's')
{
s = s - 0.5;
}
else if (set == 'b')
{
b = b - 0.2;
}
else if (set == 'r')
{
r = r - 1;
}
else if (set == 'w')
{
dw = dw - 1;
}
else if (set == 'z')
{
dz = dz - 1;
}
else if (set == 'd')
{
dim = dim - 5;
}
}
// Tell GLUT it is necessary to redisplay the scene
glutPostRedisplay();
}
void special(int key,int x,int y)
{
// Right arrow key - increase azimuth by 5 degrees
if (key == GLUT_KEY_RIGHT)
th += 5;
// Left arrow key - decrease azimuth by 5 degrees
else if (key == GLUT_KEY_LEFT)
th -= 5;
// Up arrow key - increase elevation by 5 degrees
else if (key == GLUT_KEY_UP)
ph += 5;
// Down arrow key - decrease elevation by 5 degrees
else if (key == GLUT_KEY_DOWN)
ph -= 5;
// Keep angles to +/-360 degrees
th %= 360;
ph %= 360;
// Tell GLUT it is necessary to redisplay the scene
glutPostRedisplay();
}
/*
* Display the scene
*/
void reshape(int width,int height)
{
// Ratio of the width to the height of the window
double w2h = (height>0) ? (double)width/height : 1;
// Set the viewport to the entire window
glViewport(0,0, width,height);
// Tell OpenGL we want to manipulate the projection matrix
glMatrixMode(GL_PROJECTION);
// Undo previous transformations
glLoadIdentity();
// Orthogonal projection box adjusted for the
// aspect ratio of the window
glOrtho(-dim*w2h,+dim*w2h, -dim,+dim, -dim,+dim);
// Switch to manipulating the model matrix
glMatrixMode(GL_MODELVIEW);
// Undo previous transformations
glLoadIdentity();
}
/*
* Start up GLUT and tell it what to do
*/
int main(int argc,char* argv[])
{
// Initialize GLUT and process user parameters
glutInit(&argc,argv);
// Request double buffered, true color window
glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);
glutInitWindowPosition(50, 50);
// Request 500 x 500 pixel window
glutInitWindowSize(500,500);
// Create the window
glutCreateWindow("Lorenz Attractor");
// Tell GLUT to call "display" when the scene should be drawn
glutDisplayFunc(display);
// Tell GLUT to call "reshape" when the window is resized
glutReshapeFunc(reshape);
// Tell GLUT to call "special" when an arrow key is pressed
glutSpecialFunc(special);
// Tell GLUT to call "key" when a key is pressed
glutKeyboardFunc(key);
// Tell GLUT to call "key" when a key is pressed
glutMainLoop();
// Return code
return 0;
}
