Methods for generating meshes with sharp features

Abstract

Computer graphics applications call for various mesh generation techniques to visualize objects, store shape data, perform numerical analyses, etc. Mesh generation is also a fundamental research topic in many other engineering areas related to physical models described by partial differential equations. The reason that meshed surfaces are preferred over spline surfaces in many engineering applications is its flexibility in handling complex objects, while sharp features and boundaries can be represented without trimming, which is highly desired in numerical simulations.

In this thesis, we study two methods for generating meshes with sharp features. Sharp features, such as creases and corners, are very common in mechanical objects. Hence effectively handling sharp features is of great importance to this kind of objects.

The first method is to generate triangular subdivision surfaces with sharp features. Although there have been various methods to fit subdivision surfaces to different types of shape data, e.g., dense meshes and point clouds, none of these methods can handle sharp features effectively. We present a new exact evaluation scheme for all types of sharp features in Loop subdivision, and integrate the new evaluation scheme into the optimization framework to fit Loop subdivision surfaces to dense meshes.

The second method is to generate quadrilateral meshes with varying element sizes which observe the user requirement. This method is inspired by the idea of spectral quadrangulation, but existing spectral quadrangulation methods are limited to closed surfaces due to its lack of proper boundary treatment. We present a new set of boundary conditions, and introduce the Quasi-Eigenfunction to assist the mesh generation process. The proposed boundary treatment is further applied to sharp features to handle mechanical objects. The quasi-eigenfunction based quadrangulation framework is also extended to 3D volumetric domain to generate hexahedral meshes.

Experimental results and comparisons with existing methods are presented in each chapter to demonstrate the effectiveness of the proposed methods.