On global continuity of Coons mappings in patching CAD surfaces

摘要

We tessellate a closed surface bounding a solid into four-sided patches P_i. Each patch P_i is the image of the unit square by γ_i which is the composition of a 2D Coons mapping and a bivariate function coming from a trimmed surface. Here, we concentrate on the analysis of the global continuity of the mappings γ_i over the whole surface. While using Coons functions to generate the mappings γ_i, arc length parametrization ensures that the images of the functions γ_i match pointwise at surface joints independently of the blending functions. We will describe a reparametrization technique based on cubic Bezier whose goal is to keep the shape of the initial curves while achieving arc length parametrization. The required accuracy of length computation is shown in L~∞-norm in order not to deteriorate the accuracy of the cubic spline approximation. Practical results from simulated and real CAD data which come from IGES files are reported.