New Techniques for the Modeling, Processing and Visualization of Surfaces and Volumes

Abstract

With the advent of powerful 3D acquisition technology, there is agrowing demand for the modeling, processing, and visualization ofsurfaces and volumes. The proposed methods must be efficient androbust, and they must be able to extract the essential structure ofthe data and to easily and quickly convey the most significantinformation to a human observer. Independent of the specific nature ofthe data, the following fundamental problems can be identified: shapereconstruction from discrete samples, data analysis, and datacompression.This thesis presents several novel solutions to these problems forsurfaces (Part I) and volumes (Part II). For surfaces, we adopt thewell-known triangle mesh representation and develop new algorithms fordiscrete curvature estimation, detection of feature lines, andline-art rendering (Chapter 3), for connectivity encoding (Chapter 4),and for topology preserving compression of 2D vector fields (Chapter5). For volumes, that are often given as discrete samples, we base ourapproach for reconstruction and visualization on the use of newtrivariate spline spaces on a certain tetrahedral partition. We studythe properties of the new spline spaces (Chapter 7) and presentefficient algorithms for reconstruction and visualization byiso-surface rendering for both, regularly (Chapter 8) and irregularly(Chapter 9) distributed data samples.