Modeling of Surfaces with Fair Reflection Line Pattern

Inspection of reflection line patterns is a standard way to check the quality of free form surfaces. In this paper, we describe an approach which enables the designer to control during the modeling process the reflection line pattern by approximating a specified family of reflection lines. Our method directly operates on the commonly used B-spline format, and produces fair surfaces. The approach is based on the minimization of a suitable error functional. A minimization algorithm based on data dependent quadratic error functionals provides an efficient numerical solution. The potential of the method will be demonstrated by applying it to two standard modeling problems: “surface fairing” and “surface reconstruction”.