Surface parametrization and curvature measurement of arbitrary 3-D objects: five practical methods

Abstract

Curvature sampling of arbitrary, fully described 3-D objects (e.g. tomographic medical images) is difficult because of surface patch parameterization problems. Five practical solutions are presented and characterized-the Sander-Zucker approach, two novel methods based on direct surface mapping, a piecewise linear manifold technique, and a turtle geometry method. One of the new methods, called the cross patch (CP) method, is shown to be very fast, robust in the presence of noise, and is always based on a proper surface parameterization, provided the perturbations of the surface over the patch neighborhood are isotropically distributed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>