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We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2-manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given… (More)

Discrete Laplace operators are ubiquitous in applications spanning geometric modeling to simulation. For robust-ness and efficiency, many applications require discrete operators that retain key structural properties inherent to the continuous setting. Building on the smooth setting, we present a set of natural properties for discrete Laplace operators for… (More)

We introduce FreeLence, a novel and simple single-rate compression coder for triangle manifold meshes. Our method uses free valences and exploits geometric information for connectivity encoding. Furthermore, we introduce a novel linear prediction scheme for geometry compression of 3D meshes. Together, these approaches yield a significant entropy reduction… (More)

We present a novel algorithm for automatic parameteriza-tion of tube-like surfaces of arbitrary genus such as the surfaces of knots, trees, blood vessels, neurons, or any tubular graph with a globally consistent stripe texture. Mathematically these surfaces can be described as thickened graphs, and the calculated parameterization stripe will follow either… (More)

Multiresolution meshes provide an efficient and structured representation of geometric objects. To increase the mesh resolution only at vital parts of the object, adaptive refinement is widely used. We propose a lossless compression scheme for these adaptive structures that exploits the parent-child relationships inherent to the mesh hierarchy. We use the… (More)

Figure 1. Adaptive refinement of a bone model. Elements are colored according to our coding scheme. We store a bit for every blue and red triangle, specifying whether it is further refined or not. These bits are sufficient to reconstruct the connectivity of the model. All other triangles can be reconstructed using rules of the refinement scheme as explained… (More)

for processing the Aphrodite model using QuadCover [11]. Last but not least, thanks to Peter and Mathieu for letting me wander.. . Abstract Connections provide a way to compare local quantities defined at different points of a geometric space. This thesis develops a discrete theory of connections that naturally leads to practical, efficient numerical… (More)

- Eitan Grinspun, Max Wardetzky LECTURERS, Mathieu Desbrun, Peter Schröder, Max Wardetzky, Felix Kälberer +3 others
- 2008

Preface The behavior of physical systems is typically described by a set of continuous equations using tools such as geometric mechanics and differential geometry to analyze and capture their properties. For purposes of computation one must derive discrete (in space and time) representations of the underlying equations. Researchers in a variety of areas… (More)

Triangle meshes are the basic primitives of computer graphics and many simulation algorithms. When representing complex shapes, detailed triangle meshes consume a large amount of storage in a raw data format. Increasing geometric detail in the computer aided design industry, the movie industry and in models produced by modern 3D scanners demand for… (More)

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