Fitting Unstructured Triangle Meshes Using Subdivision Surfaces

Abstract

Approximation, interpolation, and fitting are three fundamental topics in CAGD.

Appendices

Remarks

This chapter discusses several methods for subdivision surface fitting/remeshing based on C-C subdivision. In addition to the methods discussed here, there are other approaches to fitting/remeshing that use subdivision techniques, for example, Eck’s Harmonic Mapping Method for Remeshing and Ma’s Linear Least Square Method for Surface Fitting. There are also published studies in the literature [59–61, 119, 121] that use triangle subdivision schemes, particularly Loop subdivision schemes. Jeong [121] described construction of a mesh surface with Loop subdivision connectivity directly from unorganized points. Studies [63, 65, 119] have also provided approaches for the construction of sharp features for fitting surfaces and fitting meshes. It is probably important to design a specialized subdivision method for sharp features in order to obtain good fitting effects. For any fitting method, and especially for the iterative methods given in Sects. 10.1 and  10.2, the base mesh is fundamental. Base mesh shape has profound effects on the shape of the fitting surface and fitting mesh. Eck’s method is one that is widely applied to partition data points and construct base meshes. Fitting surfaces and fitting meshes of good quality are essential requirements in reverse engineering.

Exercises

• 1. For a STL original mesh, see Fig. 10.1, (i) decimate the original mesh and obtain a coarse triangle mesh and (ii) convert the coarse triangle mesh to a quadrilateral mesh using the method in Sect. 10.1.3.

• 2. Write program codes to fit the original mesh using the SLP method.