Contour generators of evolving implicit surfaces

Abstract

The contour generator is an important visibility feature of a smooth object seen under parallel projection. It is the curve on the surface which seperates front-facing regions from back facing regions. The apparent contour is the projection of the contour generator onto a plane perpendicular to the view direction. Both curves play an important role in computer graphics.Our goal is to obtain fast and robust algorithms that compute the contour generator with a guarantee of topological correctness. To this end, we first study the singularities of the contour generator and the apparent contour, for generic views, and for generic time-dependent projections, e.g. when the surface is rotated or deformed. The singularities indicate when components of the contour generator merge or split as time evolves.We present an algorithm to compute an initial contour generator, using a dynamic step size. An interval test guarantees the topological correctness. This initial contour generator can then be maintained under a time-dependent projection by examining its singularities.