Watertight Tessellation of B-rep NURBS CAD- Models using connectivity information

Abstract — This paper presents a fast method to avoid cracks between two adjacent NURBS-surfaces which are part of a boundary-represented 3D-object during the tessellation process. The surfaces are first divided into almost flat regions, then trimmings curves are split at the patch borders and finally intersection points are transferred to the opposite surface by using a priori connectivity information. This algorithm covers curved surfaces as well as curved surface boundaries. Since curvature elimination of 3D boundary curves can’t be performed well in the parameter space, it is necessary to analyze 3D curves directly. For systems where explicit knowledge of 3D boundary curves is not available this step could be a time-consuming task. Our algorithm overcomes this problem by introducing points on the boundary only if the curvature of one of the opposite surfaces requires this, which finally leads to a common boundary polygon that corresponds to the boundary curve’s curvature. Additionally each step preserves the relation between the analytical and the polygonal model what offers several advantages. It allows to decide which points and triangles should be removed to create two kinds of topology preserving Level Of Detail (LOD). First a triangle-LOD for visualization purposes and a second polygonal-LOD that is used in some CAD modules. Topology information further allows to add additional points incrementally when the finest polygonal representation is found to be to coarse