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Smooth Shape-Aware Functions with Controlled Extrema
(The Eurographics Association and Blackwell Publishing Ltd., 2012)
Functions that optimize Laplacian-based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multiscale kernel construction and interpolation. Minimizers of Dirichlet energies, or ...
Can Mean-Curvature Flow be Modified to be Non-singular?
(The Eurographics Association and Blackwell Publishing Ltd., 2012)
This work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in ...
Visualizing Robustness of Critical Points for 2D Time-Varying Vector Fields
(The Eurographics Association and Blackwell Publishing Ltd., 2013)
Analyzing critical points and their temporal evolutions plays a crucial role in understanding the behavior of vector fields. A key challenge is to quantify the stability of critical points: more stable points may represent ...
Towards Multifield Scalar Topology Based on Pareto Optimality
(The Eurographics Association and Blackwell Publishing Ltd., 2013)
How can the notion of topological structures for single scalar fields be extended to multifields? In this paper we propose a definition for such structures using the concepts of Pareto optimality and Pareto dominance. Given ...