An optimization algorithm for free-form surface partitioning based on weighted gaussian image

Partitioning free-form surfaces into sub-patches and finding optimal representative normal for each patch to maximize a global objective function is an important two-level operation in diverse industrial applications. In this paper, by solving a maximum hemispherical partitioning problem raised from a weighted Gaussian image, an optimization algorithm is proposed to partition a free-form surface into two sub-patches and simultaneously report the optimal representative normals. By discretizing the free-form surface with W sample points and clustering normals on the surface with m distinct sample normals, the proposed algorithm is designed, in general, with O(m2W2) time complexity and O(W2) space complexity, and in particular, if the surface is convex, in O(m2 log m) time complexity. Case studies with four representative examples are presented and a real world application is exploited to demonstrate the effectiveness and usefulness of the proposed algorithm.