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Consider a dense sampling S of the smooth boundary of a planar shape O, i.e., an open subset of R-2. We show that the medial axis of the union of Voronoi balls centered at Voronoi vertices inside O has a particularly simple structure: it is the union of al ...
This note illustrates how Voronoi diagrams and Delaunay triangula- tions of point sets can be computed by applying parametric linear pro- gramming techniques. We specify parametric linear programming prob- lems that yield the Delaunay triangulation or the ...
We define a new filtration of the Delaunay triangulation of a finite set of points in &Rdbl;d, similar to the alpha shape filtration. The new filtration is parameterized by a local scale parameter instead of the global scale parameter in alpha s ...
Conformal alpha shapes are a new filtration of the Delaunay triangulation of a finite set of points in &Rdbl;d. In contrast to (ordinary) alpha shapes the new filtration is parameterized by a local scale parameter instead of the global scale par ...
The distinct element method (DEM) is an approach to modelling and simulation well suited to the study of discontinuous phenomena. By tracking each element individually and dealing explicitly with every interaction among the elements, the DEM allows one to ...
During the last 20 years, the joint expansion of computing power, computer graphics, networking capabilities and multiresolution analysis have stimulated several research domains, and developed the need for new types of data such as 3D models, i.e. discret ...
In this paper, we present an original non-linear subdivision scheme suitable for univariate data, plane curves and discrete triangulated surfaces, while keeping the complexity acceptable. The proposed technique is compared to linear subdivision methods hav ...
Computer simulations of granular materials based on the distinct element method (DEM) are now commonly used in the design and optimization of industrial processes. One of the leading mathematical approach to DEM uses dynamic triangulations for detecting co ...
Granular materials are omnipresent in many fields ranging from civil engineering to food, mining and pharmaceutical industries. Often considered a fourth state of matter, they exhibit specific phenomena such as segregation, arching effects, pattern formati ...
This paper introduces the notion of Voronoi diagrams and Delaunay triangulations generated by the vertices of a piecewise flat, triangulated surface. Based on properties of such structures, a generalized flip algorithm to construct the Delaunay triangulati ...
