Centroidal Voronoi tessellations and optimal Delaunay triangulations can be approximated efficiently by non-linear optimisation algorithms. This paper demonstrates that the point distribution used to initialise the optimisation algorithms is important. Compared to conventional random initialisation, certain low-discrepancy point distributions help convergence towards more spatially regular resu...

Owing to the natural interpretation and various desirable mathematical properties, centroidal Voronoi tessellations (CVTs) have found a wide range of applications correspondingly vast development in their literature. However, computation CVTs higher dimensional spaces remains difficult. In this paper, we exploit non-uniqueness for computation. We construct such high by decomposing into one-dime...

An incremental Delaunay triangulation algorithm to generate Voronoi diagrams within the L∞ norm is presented. The main qualities are the preservation of the simplicity of the classical L2 version and its its intrinsic robustness It is then coupled to the well known Lloyd algorithm for computing Centroidal Voronoi Tesselations of point sets. This algorithm is then used to generate well shaped qu...

Proper orthogonal decompositions (POD) have been used to systematically extract the most energetic modes while centroidal Voronoi tessellations (CVT) have been used to systematically extract best representatives. We combine the ideas of CVT and POD into a hybrid method for model reduction. The optimality of such an approach and various practical implementation strategies are discussed.

A recently developed Centroidal Voronoi Tessellation (CVT) sampling method is investigated here to assess its suitability for use in statistical sampling applications. CVT efficiently generates a highly uniform distribution of sample points over arbitrarily shaped M-Dimensional parameter spaces. On several 2-D test problems CVT has recently been found to provide exceedingly effective and effici...

Proper orthogonal decompositons (POD) have been used to systematically extract the most energetic modes while centroidal Voronoi tessellations has been used to systematically extract best representatives. We combine the ideas of CVT and POD into a hybird method for model reduction. The optimality of such an approach and various practical implementation strategies are discussed.

OBJECTIVES To investigate the impacts of the different three-dimensional CT (3DCT) scanning modes on the GTV delineation for solitary pulmonary lesion (SPL) based on four-dimensional CT (4DCT), and to evaluate the feasibility of using the spiral CT scan in CT simulation. MATERIALS AND METHODS Twenty-one patients with SPL underwent axial CT scan, spiral CT scan and 4DCT simulation scan during ...

Abstract We introduce a class of systems Hamilton-Jacobi equations characterizing geodesic centroidal tessellations, i.e., tessellations domains with respect to distances where generators and centroids coincide. Typical examples are given by Voronoi power diagrams. An appropriate version the Fast Marching method on unstructured grids allows computing solution system and, therefore, associated t...