Hole patching in 3D unstructured surface mesh [electronic resource] /

by Kumar, Amitesh.

A three-dimensional object of interest in a volumetric data can be visualized using direct surface rendering methods or volume rendering approaches. Volume rendering is a visualization technique without providing the geometry information at all. However, an engineering analysis requires watertight surface geometry information of the object. Thus a three-dimensional object representation for the visualization using direct surface rendering may not necessarily be valid for engineering analysis, as such models are not necessarily watertight. Obtaining watertight surfaces has been a challenging task in the field of computational engineering due to presence of deficiencies such as gaps and holes in the surfaces. The focus of this thesis is to address the need to patch holes in the surfaces to obtain a watertight geometry. Most of the methods available for hole patching today are limited in their utility, in most cases, by the method with which the geometric model has been originally obtained. This research work provides an innovative and original method of creating surface patches for topologically simple holes in unstructured discrete geometry using parametric NURBS (Non-Uniform Rational B-Spline) surface formulation and Delaunay criteria for point insertion and edge swapping. Surface patches are generated using existing points surrounding the holes without altering the surrounding geometry. This study is to introduce the mathematic foundation and the computer algorithm developed, along with several examples to demonstrate the success of this approach. The watertight geometry so produced has a ii wide range of engineering applications in the field of mechanical simulation studies, using either computational fluid dynamics or computational structural mechanics. iii