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Selected Readings in Vision and Graphics
edited by Luc Van Gool, Gábor Székely, Markus Gross, Bernt Schiele

Volume 24



Matthias Zwicker
Continuous Reconstruction, Rendering,
and Editing of Point-Sampled Surfaces
First edition 2003, 188 pages, € 64,00. ISBN 3-89649-876-2

The mathematical representation of surfaces is at the core of most computer graphics problems. In particular, the design of modeling and rendering algorithms for computer graphics applications is largely determined by the specific surface representation that is chosen. A variety of mathematical models has been developed for such applications, ranging from parametric to implicit surfaces. In this thesis, we propose to use nonuni­form point samples to continuously reconstruct, render, and interactively edit surfaces. Based on results from classical signal processing theory, we develop core methods for reconstructing, filtering, and resampling nonuniformly point-sampled surfaces. From these concepts, we derive algorithms for high quality, antialiased rendering and inter­active surface parameterization.
We start by reviewing fundamental signal processing theory, paying particular attention to an analysis of the aliasing phenomenon. We then derive the concept of resampling filters as an efficient antialiasing strategy. Next, we shift our attention to nonuniformly sampled signals and discuss a local filtering approach to nonuniform sampling and reconstruction. Extending these local filtering techniques and combining them with resampling filters, we introduce a parametric representation of point-sampled surfaces. We show how to interpret rendering as resampling a parameterized surface, and we derive an antialiased rendering algorithm for point-sampled surfaces. We also present an efficient, hierarchical data structure tailored for point-based rendering. We further develop a resampling filter and a splatting algorithm for volume data.
Finally, we present a framework for interactive editing of point-sampled surfaces building upon two fundamental operations, namely surface parameterization and surface resampling. We show how to implement editing operations such as painting, texturing, carving, displacement mapping, and filtering.

About the Author:
Matthias Zwicker received his MSc degree in Computer Science (Dipl. Informatik-Ing. ETH) from the Swiss Federal Institute of Technology (ETH) Zurich, Switzerland, in 1998. From 1998 to 2003, he has been a research assistant and PhD student with the Computer Graphics Laboratory at ETH Zurich. He earned his PhD in Computer Science in 2003 for his work on rendering algorithms and data structures for point-based surface representations. Currently, Matthias Zwicker is a Postdoctoral Associate with the Computer Graphics Group at the Massachusetts Institute of Technology.

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