Visualizing High-Order Surface Geometry
Abstract
We have derived parameters that describe the higher-order geometric behavior of smooth surfaces. Our parameters are similar in spirit to the principal directions and principal curvatures that succinctly capture second-order shape behavior. We derive our parameters from a cylindrical Fourier decomposition around the surface normal. We present a visualization program for studying the influence of the various terms of different degrees on the shape of the local neighborhood of a surface point. We display a small surface patch that is controlled by two sets of parameters: One set is a simple polynomial description of the surface geometry in Cartesian coordinates. The other one is a set of Fourier components grouped by angular frequency and by their phase shifts. Manipulating the values in one parameter set changes the geometry of the patch and also updates the parameter values of the other set.
Citation
Pushkar Joshi and Carlo H. Séquin. "Visualizing High-Order Surface Geometry". Computer-Aided Design and Applications, 6(2):263–268, June 2009.