Artifact analysis on B-splines, box-splines and other surfaces defined by quadrilateral polyhedra

Abstract

When using NURBS or subdivision surfaces as a design tool in engineering applications, designers face certain challenges. One of these is the presence of artifacts. An artifact is a feature of the surface that cannot be avoided by movement of control points by the designer. This implies that the surface contains spatial frequencies greater than one cycle per two control points. These are seen as ripples in the surface and are found in NURBS and subdivision surfaces and potentially in all surfaces specified in terms of polyhedrons of control points. Ideally, this difference between designer intent and what emerges as a surface should be eliminated. The first step to achieving this is by understanding and quantifying the artifact observed in the surface. We present methods for analysing the magnitude of artifacts in a surface defined by a quadrilateral control mesh. We use the subdivision process as a tool for analysis. Our results provide a measure of surface artifacts with respect to initial control point sampling for all B-Splines, quadrilateral box-spline surfaces and regular regions of subdivision surfaces. We use four subdivision schemes as working examples: the three box-spline subdivision schemes, Catmull–Clark (cubic B-spline), 4-3, 4-8; and Kobbeltʼs interpolating scheme.