Book Image

Mathematics for Game Programming and Computer Graphics

By : Penny de Byl
5 (1)
Book Image

Mathematics for Game Programming and Computer Graphics

5 (1)
By: Penny de Byl

Overview of this book

Mathematics is an essential skill when it comes to graphics and game development, particularly if you want to understand the generation of real-time computer graphics and the manipulation of objects and environments in a detailed way. Python, together with Pygame and PyOpenGL, provides you with the opportunity to explore these features under the hood, revealing how computers generate and manipulate 3D environments. Mathematics for Game Programming and Computer Graphics is an exhaustive guide to getting “back to the basics” of mathematics, using a series of problem-based, practical exercises to explore ideas around drawing graphic lines and shapes, applying vectors and vertices, constructing and rendering meshes, and working with vertex shaders. By leveraging Python, Pygame, and PyOpenGL, you’ll be able to create your own mathematics-based engine and API that will be used throughout to build applications. By the end of this graphics focussed book, you’ll have gained a thorough understanding of how essential mathematics is for creating, rendering, and manipulating 3D virtual environments and know the secrets behind today’s top graphics and game engines.
Table of Contents (26 chapters)
1
Part 1 – Essential Tools
9
Part 2 – Essential Trigonometry
14
Part 3 – Essential Transformations
20
Part 4 – Essential Rendering Techniques

Summary

You are now an expert at opening graphics windows and have new-found skills at plotting pixels in that window using Cartesian coordinates. This skill is the essential underpinning of everything that gets drawn on a computer screen; it’s through the understanding of mathematics that you will gain throughout this book that you will be able to expand that single pixel into a world of complex 3D structures, colors, and animations. Some of these basic graphics primitives will be explored in the following chapter.

Answers

Exercise A:

import pygame
pygame.init()
screen_width = 900
screen_height = 500
screen = pygame.display.set_mode((screen_width, screen_height))
done = False
white = pygame.Color(255, 255, 255)
def draw_star(x, y, size):
  pygame.draw.rect(screen, white, (x, y, size, size))
while not done:
  for event in pygame.event.get():
    if event.type == pygame.QUIT:
      done = True
  draw_star (121, 320, 15)
  draw_star (327, 324, 15)
  draw_star (691, 431, 20)
  draw_star (697, 317, 10)
  draw_star (626, 246, 30)
  draw_star (343, 212, 10)
  draw_star (653, 165, 10)
  draw_star (773, 102, 10)
  draw_star (822, 153, 10)
  pygame.display.update()
pygame.quit()