sierpinski2d.cpp

// This program generates a Sierpinski gasket with 10000 points.

#ifdef __APPLE_CC__
#include <GLUT/glut.h>
#else
#include <GL/glut.h>
#endif
#include <cstdlib>

// A simple two-dimensional point class to make life easy.  It allows you to
// reference points with x and y coordinates instead of array indices) and
// encapsulates a midpoint function.
struct Point {
  GLfloat x, y;
  Point(GLfloat x = 0, GLfloat y = 0): x(x), y(y) {}
  Point midpoint(Point p) {return Point((x + p.x) / 2.0, (y + p.y) / 2.0);}
};

// Draws a Sierpinski triangle with a fixed number of points. (Note that the
// number of points is kept fairly small because a display callback should
// NEVER run for too long.
void display() {

  glClear(GL_COLOR_BUFFER_BIT);

  static Point vertices[] = {Point(0, 0), Point(200, 500), Point(500, 0)};

  // Compute and plot 100000 new points, starting (arbitrarily) with one of
  // the vertices. Each point is halfway between the previous point and a
  // randomly chosen vertex.
  static Point p = vertices[0];
  glBegin(GL_POINTS);
  for (int k = 0; k < 100000; k++) {
    p = p.midpoint(vertices[rand() % 3]);
    glVertex2f(p.x, p.y);
  }
  glEnd();
  glFlush();
}

// Performs application-specific initialization. Sets colors and sets up a
// simple orthographic projection.
void init() {

  // Set a deep purple background and draw in a greenish yellow.
  glClearColor(0.25, 0.0, 0.2, 1.0);
  glColor3f(0.6, 1.0, 0.0);

  // Set up the viewing volume: 500 x 500 x 1 window with origin lower left.
  glMatrixMode(GL_PROJECTION);
  glLoadIdentity();
  glOrtho(0.0, 500.0, 0.0, 500.0, 0.0, 1.0);
}

// Initializes GLUT, the display mode, and main window; registers callbacks;
// does application initialization; enters the main event loop.
int main(int argc, char** argv) {
  glutInit(&argc, argv);
  glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB);
  glutInitWindowSize(500, 500);
  glutInitWindowPosition(40, 40);
  glutCreateWindow("Sierpinski Triangle");
  glutDisplayFunc(display);
  init();
  glutMainLoop();
}