Chapter 1 - Introduction

Abstract

The most common reason for not being able to implement a solution is the lack of understanding of computer graphics principles. Computer graphics is based on mathematics and many people are quite reluctant to learn it. A common reason for this is that the mathematics is presented in abstract and theoretical terms with little application to solving real-world problems. This chapter introduces the most important fundamental mathematical concepts without diverging into esoteric mathematical areas that have little practical use. The explanation of each mathematical concept also involves source code and scripts that demonstrate the implementation of the concept. The entire spectrum of computer graphics concepts through geometry and modeling is also covered. The process of transforming (scaling, shearing, rotating, translating, and projecting) objects is an integral part of computer graphics. Transformations are most efficiently implemented using matrices and are covered in the later stages of the book. The most fundamental building blocks of computer graphics are points and vectors. Geometry uses points and vectors to represent more complex shapes such as curves and surfaces. The chapter also highlights subdivision surfaces—a popular geometry type—which is discussed in detail in the later stages of the book.