Intersection and Trimming of Subdivision Surfaces

Abstract

Based on the multiresolution approximation and piecewise parameterization representation of subdivision surfaces, this chapter introduces precise intersection and trimming algorithms.

Appendices

Remarks

Intersection and trimming are the most fundamental and important operations in CAD/CAM, and are widely applied in surface offsetting, interference inspection, and Boolean operations in solid modeling. The quality of the intersection and trimming thus impacts significantly on the robustness and applicability of the whole system. This chapter introduced two algorithms for intersection and trimming of subdivision surfaces: approximation representation with control meshes at certain subdivision levels, and piecewise parametric representation. The region of Boolean operations is closely related to intersection and trimming. Consequently, in addition to the work discussed in this chapter, there are other publications referring to intersection and trimming. For example, Litke [54] presents a trimming method for subdivision surfaces; Biermann [68] discusses Boolean operations on solids that are represented by subdivision surfaces; and Zhou [70] provides methods for intersection and trimming. The discussions in these publications are based on triangular subdivisions. Hui [69] describes a smooth blending method for C-C subdivision surfaces; blending of two surfaces can be regarded as a union operation.

Exercises

Give a concise process for the intersection operation of two subdivision surfaces according to the discussion of this chapter.