Graphics Gems V (IBM Version)

II.7

Distance Approximations and Bounding Polyhedra

Wm. Paeth Alan,     Department of Computer Science Okanagan University College Kelowna, British Columbia. E-mail address: [e-mail]

Introduction

This gem presents an n-dimensional linear approximation that can only overestimate distance, preserving the valuable containment property of the previous 2D method (Paeth 1990a). Whereas the latter was solved using trigonometry, this gem employs geometric methods to derive a family of semiregular polytopes having cubic symmetry. These solids provide a nested sequence of bounding that encases the n-sphere: that locus of points in n-space lying at a unit distance from the origin. As a bonus, the gem provides geometric insight and illustration ...