Graphics Gems V (IBM Version)

I.1

Solving Quartics and Cubics for Graphics

Herbison-Evans Don,     Central Queensland University Bundaberg Campus. E-mail address: [e-mail]

Introduction

In principle, quartic and cubic equations can be solved without using iterative techniques. In practice, most numerical algorithms based directly upon analytic solutions of these equations are neither well-behaved nor efficient. This gem ¹ derives a robust C-language implementation based upon the solutions of Neumark and Ferrari. Its superiority in controlling both round-off error and overflow is also demonstrated.

Background

Quartic equations need to be solved when ray tracing fourth-degree surfaces, e.g., a torus. Quartics also need to be solved in a number of problems ...