Third Eurographics Symposium on Geometry Processing
in cooperation with ACM SIGGRAPH

Invited speakers

The conference featured three prominent researchers as keynote speakers:

Herbert Edelsbrunner, Duke University

Surface Tiling with Differential Topology

A challenging problem in computer-aided geometric design is the tiling of a surface into quadrangular regions that can then be represented by NURBS patches. There are various approaches published in the literature and commercially available software, but all fall short in either automation or quality of the tiling. At Raindrop Geomagic, we take a fresh approach based on concepts from Morse theory. This by itself is not a new idea, but we need some novel ingredients to make this work, one being a rational notion of hierarchy that guides the construction of a simplified partition sensitive to only the major critical points. This talk will present the main steps of the tiling algorithm, such as defining the function, partitioning the surface, forming blending patches, and finally decomposing the regions into quadrangles. It will illustrate the work-flow with examples and discuss some of the difficulties that arise.

This talk will present the main steps of the segmentation algorithm, such as defining the function, segmenting the surface, forming the blending surfaces, and tiling the rest into quadrangles. It will discuss some of the difficulties that arise, and it will present plenty of examples.

Marc Alexa, Technische Universit?Darmstadt

Non-conforming surface representations

Surface geometry is commonly represented by a collection of primitives. Conforming representations consist of primitives meeting at their boundaries (e.g., in a triangle mesh two triangles are incident upon an edge). Without the restriction to conforming elements there are no dependencies among primitives, leading to more degrees of freedom for each primitive. This yields more efficient and flexible algorithms for reconstruction, processing, and rendering, as well as compact and accurate representations.


Luis Velho, Instituto de Matematica Pura e Aplicada

Modeling with Simplicial Diffeomorphisms

In this talk I will present a new framework for geometric modeling that combines implicit and parametric surface representations with volumetric warpings. The framework is based on dynamic, adaptive simplicial decompositions of the embedding space and conforming piecewise diffeomorphisms. I will also discuss some applications and open issues related to simplicial diffeomorphisms. (This is joint work with my PhD student Vinicius Mello.)


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