Splines for Meshes with Irregularities
Jörg Peters
Abstract
Splines form an elegant bridge between the continuous real world and the discrete computational world. Their tensor-product form lifts many univariate properties effortlessly to the surfaces, volumes and beyond. Irregularities, where the tensor-structure breaks down, therefore deserve attention – and provide a rich source of mathematical challenges and insights. This paper reviews and categorizes techniques for splines on meshes with irregularities. Of particular interest are quad-dominant meshes that can have <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≠</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> valent interior points and T-junctions where quad-strips end. “Generalized” splines can use quad-dominant meshes as control nets both for modeling geometry and to support engineering analysis without additional meshing.