Parameter Aligned Trimmed Surfaces

Abstract

We present a new representation for trimmed parametric surfaces. Given a set of trimming curves in the parametric domain of a surface, our method locally reparametrizes the parameter space to permit accurate representation of these features without partitioning the surface into subsurfaces. Instead, the parameter space is segmented into subspaces containing the trimming curves, the boundaries of which are aligned to the local parameter axes. When multiple trimming curves are present, intersecting subspaces are further segmented using local Voronoı̈ curve diagrams which allows the subspace to be distributed equally between the trimming curves. Transition patches are then used to reparametrize the areas around the trimming curves to accommodate the trimmed edges. This allows for high quality interpolation of the trimmed edges while still allowing parametric referencing and trimmed surface sampling.