Dimensionality Paradigm for Surface Interrogations

摘要

A paradigm is proposed for analyzing problems involving complex curved surfaces in a manner suitable for practical implementation. Rather than deriving closed-form expressions for certain surfaces and problems, the problem is reformulated in a higher-dimensional space with more variables but simpler equations, thus avoiding complex symbolic manipulation and numerically delicate operations. In particular, the formation of offsets, spherical blends of fixed or variable radius, and Voronoi surfaces are considered.