Computer Graphics

Computer Graphics: from Pixels to Scenes

Matthew O. Ward Computer Science Department Worcester Polytechnic Institute

Abstract

Computer graphics is the process of creating a visual presentation of an object or scene using a mapping process from the object or data space to the image space. In its most abstract form, it involves deciding what color to set each value in a two-dimensional array which is then output to a screen or printer. Traditionally, graphics is taught by starting with 2-D line drawings and proceeding to 3-D wire frame images and finally shaded surfaces. This mimics to some extent the evolution of the field, which was based predominantly on the hardware technology available. Given the current predominance of raster-based graphics and the computational capabilities of the computers in common use, it is time for this order of presentation to be reevaluated. This manuscript approaches the teaching of graphics by starting with the generation of a pixel and builds the framework for the modeling and rendering of more and more complex 3-D objects, with minimal emphasis on two- and three-dimensional line drawing. It is hoped that this order of presentation will allow students to more quickly and effectively learn about the synthesis of pseudo-realistic 3-D images.

Contents

1 A Digital Image is Worth a Megabyte (or so) 2 The Mathematics that Make Graphics Work 3 When Light Hits a Surface 4 Building a Scene - Lots of Simple Parts 5 The Object, The World, and the Eye 6 Clipping to the Field of View 7 Perspective Projection and Arbitrary Viewing 8 Introduction to Ray Tracing 9 Curved and Fractal Surfaces 10 Solid Modeling

2 8 12 17 21 26 32 37 42 48

1

Chapter 1

A Digital Image is Worth a Megabyte (or so)
A digital image (also called a computer picture or raster) is a two-dimensional array of entities known as pixels (picture elements). A pixel is simply a numeric value, and with this value is associated a color or intensity. This...