Filling Free-Form n-Sided Holes toward Blending and Decoration

A new approach to G1 filling of n-sided holes with free-form boundary curves (e.g., polynomial, rational, sinusoidal or other parametric forms) is presented. It has no intrinsic limitation but adequate freedoms for shape adjustment and optimization. The given n-sided hole is filled by rotating a cubic Bézier curve C around a fixed unit vector nc at a fixed center point c of the hole. C´s two end points fall on the hole boundary and c respectively. nc is C´s normal at c. In this way n triangular surfaces are generated in G0 contact. Then each crease between two adjacent triangular surfaces is smoothed by sweeping another cubic Bézier curve along the crease. Thus n leafy blending patches are produced to replace the overlapped parts of the triangular surfaces. The proposed algorithm is applied to some typical examples of hole-filling on free-form surfaces, such as blending and decoration.