Time for action – drawing the Sierpinski gasket

For the purpose of demonstration we will draw a Sierpinski gasket, also known as Sierpinski triangle or Sierpinski Sieve with OpenGL. This is a fractal pattern in the shape of a triangle created by the mathematician Waclaw Sierpinski. The triangle is obtained via a recursive and, in principle, infinite procedure. Perform the following steps to draw the Sierpinski gasket:

  1. First, we will start out by initializing some of the OpenGL-related primitives. This includes setting the display mode and background color. A line-by-line explanation is given at the end of this section.
    def display_openGL(w, h):
  pygame.display.set_mode((w,h), pygame.OPENGL|pygame.DOUBLEBUF)

  glClearColor(0.0, 0.0, 0.0, 1.0)
  glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT)
  
  gluOrtho2D(0, w, 0, h)
  2. The algorithm requires us to display points, the more the better. First, we set the drawing color to red. Second, we define the vertices (I call them points myself) of a triangle. Then we define random indices, which are to be used to choose one of the three triangle vertices. We pick a random point somewhere in the middle – it doesn't really matter where. After that we draw points halfway between the previous point and one of the vertices picked at random. Finally, we "flush" the result.
        glColor3f(1.0, 0, 0)
    vertices = np.array([[0, 0], [DIM/2, DIM], [DIM, 0]])
    NPOINTS = 9000
    indices = np.random.random_integers(0, 2, NPOINTS)
    point = [175.0, 150.0]

    for i in xrange(NPOINTS):
        glBegin(GL_POINTS)
        point = (point + vertices[indices[i]])/2.0glVertex2fv(point)
        glEnd()

    glFlush()

    The Sierpinski triangle looks like the following screenshot:

    Time for action – drawing the Sierpinski gasket

    The following is the full Sierpinski gasket demo code with all the imports:

    import pygame
from pygame.locals import *
import numpy as np
     
from OpenGL.GL import *
from OpenGL.GLU import *

def display_openGL(w, h):
  pygame.display.set_mode((w,h), pygame.OPENGL|pygame.DOUBLEBUF)

  glClearColor(0.0, 0.0, 0.0, 1.0)
  glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT)

  
  gluOrtho2D(0, w, 0, h)

def main():
    pygame.init()
    pygame.display.set_caption('OpenGL Demo')
    DIM = 400
    display_openGL(DIM, DIM)
    glColor3f(1.0, 0, 0)
    vertices = np.array([[0, 0], [DIM/2, DIM], [DIM, 0]])
    NPOINTS = 9000
    indices = np.random.random_integers(0, 2, NPOINTS)
    point = [175.0, 150.0]

    for i in xrange(NPOINTS):
       glBegin(GL_POINTS)
       point = (point + vertices[indices[i]])/2.0
       glVertex2fv(point)
       glEnd()

    glFlush()
    pygame.display.flip()
     
    while True:
        for event in pygame.event.get():
            if event.type == QUIT:
                return
    
if __name__ == '__main__':
  main()

What just happened?

As promised, the following is a line-by-line explanation of the most important parts of the example:

Function

Description

pygame.display.set_mode((w,h), pygame.OPENGL|pygame.DOUBLEBUF)

This sets the display mode to the required width, height, and OpenGL display.

glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT)

This clears the buffers using a mask. Here we clear the color buffer and depth buffer bits.

gluOrtho2D(0, w, 0, h)

This defines a 2D orthographic projection matrix with the coordinates of the left, right, top, and bottom clipping planes.

glColor3f(1.0, 0, 0)

This defines the current drawing color using three float values for RGB. In this case we will be painting in red.

glBegin(GL_POINTS)

This delimits the vertices of primitives or a group of primitives. Here the primitives are points.

glVertex2fv(point)

This renders a point given a vertex.

glEnd()

This closes a section of code started with glBegin.

glFlush()

This forces execution of GL commands.

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.
Reset