Implicitization of Biquadratic B\'ezier Triangle and Quadrilateral Surfaces

TL;DR

This paper derives implicit equations for biquadratic Bézier triangle and quadrilateral surfaces, providing computational tools to evaluate these functions efficiently using modern hardware.

Contribution

It introduces explicit implicit equations for biquadratic Bézier surfaces and offers implementation code leveraging contemporary computing resources.

Findings

Explicit implicit equations for biquadratic Bézier surfaces derived.

Efficient function evaluation code provided.

Utilizes modern computing to enhance algebraic techniques.

Abstract

We produce implicit equations for general biquadratic (order 2x2) B\'ezier triangle and quadrilateral surface patches and provide function evaluation code, using modern computing resources to exploit old algebraic construction techniques.