On global continuity of Coons mappings in patching CAD surfaces

We tessellate a closed surface bounding a solid into four-sided patches PiPi. Each patch PiPi is the image of the unit square by γi 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 γi over the whole surface. While using Coons functions to generate the mappings γi, arc length parametrization ensures that the images of the functions γi match pointwise at surface joints independently of the blending functions. We will describe a reparametrization technique based on cubic Bézier 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∞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.