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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 ...
While studies of solidification microstructures have focused mainly on the tips of the dendrites, the last stage solidification is equally important from the point of view of defect formation (porosity, hot tearing), mechanical strength build-up and precip ...
This thesis proposes novel ways both to represent the static surfaces, and to parameterize their deformations. This can be used both by automated algorithms for efficient 3–D shape reconstruction, and by graphics designers for editing and animation. Deform ...
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 ...
This paper proposes a new family of bivariate, non-separable splines, called hex-splines, especially designed for hexagonal lattices. The starting point of the construction is the indicator function of the Voronoi cell, which is used to define in a natural ...
Recently, we have proposed a novel family of bivariate, non-separable splines. These splines, called "hexsplines" have been designed to deal with hexagonally sampled data. Incorporating the shape of the Voronoi cell of a hexagonal lattice, they preserve th ...
We propose a new exact Euclidean distance transformation (DT) by propagation, using bucket sorting. A fast but approximate DT is first computed using a coarse neighborhood. A sequence of larger neighborhoods is then used to gradually improve this approxima ...
The basic concepts of a deterministic model for simulating grain growth or foam coarsening in two dimensions are presented, and the fundamental tools necessary for its implementation into computer codes are provided. It is assumed that the actual cell stru ...
The basic concepts of a deterministic scheme for simulating grain growth or foam coarsening in two dimensions have been presented in Part I. Implementation of the corresponding Laguerre (or weighted Voronoi) diagram in computer manageable practical terms i ...
An efficient adaptive algorithm is presented for a stationary regularized Stefan problem in 2D. The adaptive criteria relies upon a posteriori estimates based on the residual equation. Since the problem we are studying is a non-linear diffusion-convection ...