Real-Time Curvature-aware Re-Parametrization and Tessellation of Bézier Surfaces

Abstract

Interactive tessellation of parametric surfaces has many applications in both engineering and entertainment computing. The most common primitives are bi-cubic Bézier patches which are, among others, an intermediate representation of subdivision surfaces for rendering. The current state-of-the-art employs hardware tessellation where a uniform subdivison pattern is used per patch. If the curvature varies strongly over a patch, this results in an over-tessellation of flat areas. Based on the observation that the second derivative changes linearly over the patch, we show that it is possible to reparameterize the patches such that the tessellation adapts to the curvature. This way, we reduce the number of primitives by an average of 15% for the same error bound.