Subdivision Surfaces and Curve Networks

Abstract

Curve network interpolation is an important method for free-form surface modeling. This chapter first discusses the construction of a curve network of arbitrary topology and then introduces a technique for generation of a combined subdivision surface interpolating curve network. Finally, an improved approach to fairing is provided, and two shape modification methods for combined subdivision surfaces are described.

Appendices

Remarks

Curve network interpolation is an important free-form surface modeling method. The interpolated curves may be feature curves, section curves, or contours of the surface, whose layout and quality are key factors that influence the quality and efficiency of modeling. Coons surfaces, Gordon surfaces, and B-spline skinning methods are all based on infinite interpolation of curves and are widely used in the fields of CAD, geometric modeling, and computer graphics. However, surfaces constructed by these methods are all restricted to rectangular parameter domains, and in general it is difficult to construct a whole interpolated surface for complex models. A curve network usually has to be divided into a few small ones with rectangular topology, and the split networks are interpolated independently and stitched into a completed interpolated surface, greatly reducing the modeling efficiency. For some time, researchers have wanted to break the constraints of curve network topology and model more freely [203–205]. Subdivision surface modeling based on curve network constraints, presented in this chapter, is one example of a suitable approach. With the help of the combined subdivision scheme, we have not only described an interpolation technique with an arbitrary curve network, but have also provided a modification method based on curve constraints and an approach for fairing of combined subdivision surfaces based on discrete PDE.

Exercises

Give a concise process for the combined subdivision scheme according to the discussion of this chapter.