The Transition Between Sharp and Rounded Features and the Manipulation of Incompatible Boundary in Filling n-sided Holes

Abstract

N-sided hole filling plays an important role in vertex blending. Piegl and Tiller presented an algorithm to interpolate the given boundary and cross-boundary derivatives in B-spline form. To deal with the incompatible cases that their algorithm cannot handle, we propose an extension method to manipulate the transition between sharp and rounded features. The algorithm first patches n crescent-shaped extended surfaces to the boundary with G2 continuity to handle incompatibility problem in the corners. Then, we compute the inner curves and the corresponding cross-boundary derivatives fulfilling tangent and twist compatibilities. The generated B-spline Coons patches are G1-continuously connected exactly, and have epsilon-G1 continuity with the extended surfaces. Our method improves the continuity-quality of the shape and reduces the count of the inserted knots. It can be applied to all G0-continuous boundary conditions without any restrictions imposed on the boundary or cross-boundary derivatives. It generates better shapes than some popular industrial modeling systems on these incompatible occasions. Some examples underline its feasibility.