A General Sixth Order Geometric Partial Differential Equation and Its Application in Surface Modeling ?
نویسندگان
چکیده
In computer aided geometric design and computer graphics, high quality fair surfaces with G2 smoothness are sometimes required. In this paper we derive a general sixth order geometric partial differential equation from minimizing a curvature integral functional. The obtained equation is used to solve several surface modeling problems such as free-form surface design, surface blending and N-side hole filling, with G2 boundary constraints. We solve the equation numerically using a generalized divided difference method, where a quadratic fitting scheme is adopted to discretize several used geometric differential operators consistently. The experiments show that the proposed method is efficient and yields high quality surfaces.
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