A method for modifying a surface model with non-uniformly scattered displacement constraints for shoe sole design

This paper presents a method for modifying a surface model with non-uniformly scattered displacement constraints. When displacement vectors are given as constraints to feature points on the original surfaces, those of the other points should be computed to construct deformed surfaces. To maintain the overall appearance and smoothness of the original surfaces, the proper relationship should be formulated between the displacement vectors of feature points and those of the other points. For this purpose, a 3D vector field, a set of displacement vectors, is constructed based on the given constraints. Multi-level B-spline approximation technique is also used to circumvent a tradeoff between smoothness and accuracy. The technique uses coarse-to-fine hierarchy of control lattices. The proposed method is implemented as a module of the shoe sole design system and applied especially for shoe grading.