Implicitization of Biquadratic Bézier Triangle and Quadrilateral Surfaces

2023/01/03 by Borchardt, Jackson, Kato, Saul
#Computational Geometry (cs.CG) #FOS: Computer and information sciences

paper · doi:10.48550/arxiv.2301.01318

Abstract

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

Related

• Implicitization of surfaces in P³ in the presence of base points
• An algorithm for computing implicit equations of bigraded rational surfaces
• Surface Parametrization of Nonsimply Connected Planar Bézier Regions
• Linear-time geometric algorithm for evaluating Bézier curves
• A wide diversity of 3D surfaces Generator using a new implicit function