Wenhe Liao

Interactive Shape Editing for Subdivision Surfaces

This chapter firstly provides two free-form deformation algorithms of subdivision surfaces by combining mesh deformation with shape editing under simple geometrical constraints or potential function constraints.

Poisson Mesh Editing Guided by Subdivision Surface

This chapter firstly discusses the Poisson mesh editing method guided by subdivision surfaces and then extends it further to the mesh deformation based on surface control. The former constructs the deformation control surface by the subdivision surface determined by the mesh model which was bounded by the mesh to be deformed and converts the corresponding subdivision surface deviation information into the manipulation on the gradient field of the model.

Splines and Subdivision

Most subdivision schemes are derived from refinement methods of control meshes of spline curves and surfaces.

n-Sided Patches and Subdivision Surfaces

It is the base of surface blending and n-sided holes filling to construct n-sided patches. This chapter discusses three methods to construct n-sided patches. The first one is the manifold method. The control mesh of a manifold patch is constructed on the basis of the 5-ring submesh of an extraordinary vertex of a mesh with C-C subdivision connectivity.

Subdivision Surfaces and Curve Networks

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.

Meshes and Subdivision

By generalizing refinement rules of control meshes of spline surfaces, we can obtain many subdivision schemes of meshes with arbitrary topology.

Intersection and Trimming of Subdivision Surfaces

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

Energy Optimization Method and Subdivision Surfaces

An important research content of surface modeling is to construct fairing curves and surfaces, and the optimization modeling is an important method to construct fairing curves and surfaces, so which has been always being focused by many researchers.

Analysis of Subdivision Surface

A mesh sequence is generated when a given mesh is recursively subdivided. Consequently, two questions are always asked: Is the mesh sequence convergent? How many is the continuity order of the limit surface if the mesh sequence is convergent? The two questions will be answered in this chapter.