Graphics Gems V (IBM Version)

I.4

Rational Approximation

Shoemake Ken,     University of Pennsylvania Philadelphia, Pennsylvania. E-mail address: [e-mail]

Introduction

One way to combat accuracy losses in graphical algorithms such as intersection testing is to use rational numbers instead of floating point. For these and other purposes, the following discussion (accompanied by code) presents a way to construct a rational approximation to a floating-point number, optionally limiting the size of the integers used. The mathematical theory of best rational approximations is a necessary ingredient, but because it assumes perfect real numbers, it is not sufficient. Floating-point arithmetic must be avoided even during conversion!

Rational approximation ...