Rendering the mandelbrot set in OpenGl - c++

Question

I have to render the mandelbrot set and I was wondering if someone could point out some flaws with my code - at the moment, the output windows just shows a black screen. I think that my mandelbrot mathematics are correct, because I have used the same code to output a .tga of the mandelbrot - is it something to do with the OpenGl method I am using to output the pixels?
Full code:
#include <Windows.h>
#include <GL\glew.h>
#include <GL\freeglut.h>
#include <iostream>
#include <stdlib.h>
#include <chrono>
#include <cstdint>
#include <cstdlib>
#include <complex>
#include <fstream>
#include <thread>
#include <mutex>
#include <vector>
#include <Windows.h>
// Import things we need from the standard library
using std::chrono::duration_cast;
using std::chrono::milliseconds;
using std::complex;
using std::cout;
using std::endl;
using std::ofstream;
// ...other useful includes
using std::cout;
using std::endl;
using std::thread;
using std::mutex;
using std::lock;
using std::unique_lock;
using std::vector;
const int width = 600, height = 600; // window size
int windowID;
// The number of times to iterate before we assume that a point isn't in the
// Mandelbrot set.
// (You may need to turn this up if you zoom further into the set.)
const int MAX_ITERATIONS = 500;
bool fullScreen = false;
bool need_to_draw = true;
//****************************************
// Render the Mandelbrot set into the image array.
// The parameters specify the region on the complex plane to plot.
void compute_mandelbrot(double left, double right, double top, double bottom)
{
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); // clear the screen buffer
glBegin(GL_POINTS); // start drawing in single pixel mode
for (int y = 0; y < height; ++y)
{
for (int x = 0; x < width; ++x)
{
// Work out the point in the complex plane that
// corresponds to this pixel in the output image.
complex<double> c(left + (x * (right - left) / width),
top + (y * (bottom - top) / height));
// Start off z at (0, 0).
complex<double> z(0.0, 0.0);
// Iterate z = z^2 + c until z moves more than 2 units
// away from (0, 0), or we've iterated too many times.
int iterations = 0;
while (abs(z) < 2.0 && iterations < MAX_ITERATIONS)
{
z = (z * z) + c;
++iterations;
}
if (iterations == MAX_ITERATIONS)
{
glColor3f(1.0, 0.0, 0.0); // Set color to draw mandelbrot
// z didn't escape from the circle.
// This point is in the Mandelbrot set.
glVertex2i(x, y);
}
else
{
glColor3f(0.0, 0.0, 0.0); //Set pixel to black
// z escaped within less than MAX_ITERATIONS
// iterations. This point isn't in the set.
glVertex2i(x, y);
}
}
}
glEnd();
glutSwapBuffers();
need_to_draw = false;
}
int main(int argc, char** argv)
{
glutInit(&argc, argv);
glutInitDisplayMode(GLUT_DEPTH | GLUT_DOUBLE | GLUT_RGBA);
glClearColor(0.0f, 0.0f, 0.0f, 0.0f);
GLsizei windowX = (glutGet(GLUT_SCREEN_WIDTH) - width) / 2;
GLsizei windowY = (glutGet(GLUT_SCREEN_HEIGHT) - height) / 2;
glutInitWindowPosition(windowX, windowY);
glutInitWindowSize(width, height);
windowID = glutCreateWindow("Mandelbrot");
if (need_to_draw)
{
compute_mandelbrot(-2.0, 1.0, 1.125, -1.125);
}
glShadeModel(GL_SMOOTH);
glEnable(GL_DEPTH_TEST);
glViewport(0, 0, (GLsizei)width, (GLsizei)height);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glutMainLoop();
return 0;
}

Answer 1

The identity GL_PROJECTION matrix doesn't give you a 1-to-1 unit-to-pixel mapping like you're assuming, it's a +/-(1,1,1) cube.
Use glOrtho() to get the matrix you want:
glOrtho( 0, width, 0, height, -1, 1 );
All together:
#include <GL/glut.h>
#include <complex>
using std::complex;
// Render the Mandelbrot set into the image array.
// The parameters specify the region on the complex plane to plot.
void compute_mandelbrot( double left, double right, double top, double bottom )
{
// The number of times to iterate before we assume that a point isn't in the
// Mandelbrot set.
// (You may need to turn this up if you zoom further into the set.)
const int MAX_ITERATIONS = 500;
const int width = glutGet( GLUT_WINDOW_WIDTH );
const int height = glutGet( GLUT_WINDOW_HEIGHT );
glBegin( GL_POINTS ); // start drawing in single pixel mode
for( int y = 0; y < height; ++y )
{
for( int x = 0; x < width; ++x )
{
// Work out the point in the complex plane that
// corresponds to this pixel in the output image.
complex<double> c( left + ( x * ( right - left ) / width ),
top + ( y * ( bottom - top ) / height ) );
// Start off z at (0, 0).
complex<double> z( 0.0, 0.0 );
// Iterate z = z^2 + c until z moves more than 2 units
// away from (0, 0), or we've iterated too many times.
int iterations = 0;
while( abs( z ) < 2.0 && iterations < MAX_ITERATIONS )
{
z = ( z * z ) + c;
++iterations;
}
if( iterations == MAX_ITERATIONS )
{
glColor3f( 1.0, 0.0, 0.0 ); // Set color to draw mandelbrot
// z didn't escape from the circle.
// This point is in the Mandelbrot set.
glVertex2i( x, y );
}
else
{
glColor3f( 0.0, 0.0, 0.0 ); //Set pixel to black
// z escaped within less than MAX_ITERATIONS
// iterations. This point isn't in the set.
glVertex2i( x, y );
}
}
}
glEnd();
}
void display()
{
glClearColor( 0.0f, 0.0f, 0.0f, 0.0f );
glClear( GL_COLOR_BUFFER_BIT );
glMatrixMode( GL_PROJECTION );
glLoadIdentity();
const int width = glutGet( GLUT_WINDOW_WIDTH );
const int height = glutGet( GLUT_WINDOW_HEIGHT );
glOrtho( 0, width, 0, height, -1, 1 );
glMatrixMode( GL_MODELVIEW );
glLoadIdentity();
compute_mandelbrot( -2.0, 1.0, 1.125, -1.125 );
glutSwapBuffers();
}
int main( int argc, char** argv )
{
glutInit( &argc, argv );
glutInitDisplayMode( GLUT_DOUBLE | GLUT_RGBA );
glutInitWindowSize( 300, 300 );
glutCreateWindow( "Mandelbrot" );
glutDisplayFunc( display );
glutMainLoop();
return 0;
}