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

Answers

Exercise A:

These two triangles are similar. You only need two corresponding angles and two corresponding sides to determine this fact. Both triangles have angles of 60 and 75. This is enough to establish that the triangles are similar because if you take 60 and 75 away from 180 (the total of the angles in a triangle), then the remaining angle of K for Triangle (h) will be 45 and the corresponding angle in Triangle (g) will also be 45.

To find the length of J, you need to establish the ratio of the other corresponding sides. As the triangles are similar, you will know that the known two sides will have the same ratio – that is, 3/2 = 2.8/1.86 = 1.5.

Using this ratio, we can calculate J to be 4.8/1.5 = 3.2.

Exercise B:

This is the value of x in Triangle (j):

This is the value of x in Triangle (k):

Exercise C:

(X) To find θ, we must use the cosine rule, which, when written as a Google search, becomes arccos...