A Lightweight Tensor Product Surface Based on Cubic Bezier Curves Suitable for Interpolating Faceted Geometry

Numerical Grid Generation in Computational Field Simulations, The International Society of Grid Generation, pp.619-627, June 2002

MESHING
RESEARCH
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Abstract

A tensor surface was implemented which was based on cubic Bezier curves. The surface is defined in terms of the locations of four control points (at corners) and of the normals to the surface at those control points. The implementation that the location and gradient of the surface along each edge is dependent only on the location and normals defined at the start and end of each edge. This guarantees that surfaces sharing a common edge will be smoothly continuous. This surface is suitable for use as an interpolating mechanism within and between four-sided finite element faces. The implementation of the surface is compact occupying less than 40kb. The implementation was performed and tested in the context of the ALEGRA's [2] physlib routines and data structures.