Handbook of Computer Aided Geometric Design

Chapter 30

Direct Rendering of Freeform Surfaces

Gershon Elber

Freeform geometry has been employed in computer graphics for more than three decades. Traditionally, the rendering of freeform surfaces has been preceded by a stage in which a piecewise linear polygonal approximation is derived from the original surfaces, leaving polygons to participate in the actual rendering process.

This chapter considers some recent results on the direct rendering of freeform geometry: in other words, the rendering of freeform curves and surfaces without resorting to piecewise linear approximations.

30.1 INTRODUCTION

Surface rendering is traditionally conducted with the aid of a piecewise linear approximation. Usually, curves are sampled and displayed as polylines ...