Mathematics in Computer Graphics

Abstract

Computer graphics is a field to create pictures by computers. The origin of computer graphics was the sketchpad system developed by Sutherland (Ivan, DAC’64 Proceedings of the SHARE design automation workshop, pp 6329–6346, 1964, [1]). This system was designed to help the user to create line drawings in an intelligent way, and his work inspired many people to use computers to create synthetic images. One important research goal in computer graphics is realistic image synthesis. A tremendous amount of work has been done to achieve this goal by simulating real-world phenomena. In the early stages of the computer graphics, researchers invented many heuristic algorithms based on their intuitions to mimic the real world. However, the realism (or range of expression) obtained by those heuristic approaches was limited. Therefore, researchers started to think of simulating actual physical phenomena in order to synthesize highly realistic images. Those are what we see nowadays in movies, computer games, commercial films, etc. They could not have been achieved without the power of mathematics; mathematics has become an indispensable tool in computer graphics. We need mathematical expressions to describe the various phenomena and to numerically simulate them. In this book, the readers can understand how mathematics is used in advanced computer graphics researches. In Parts 1 and 2, we focus on appearance modeling and fluid simulation that are both hot research areas in computer graphics. Part 3 discusses the use of mathematics for digital fabrication and visualization. In each chapter, an detailed introductory lecture note is firstly provided by an expert in each research area, followed by several case studies. In this chapter, we briefly explain the purpose of these research areas.