This paper considers the interpolation for multi-dimensional data using Voronoi diagrams. Sibson's interpolant is well-known as an interpolation method using Voronoi diagrams for discretely distributed data, and it is extended to continuously distributed data by Gross. On the other hand, the authors studied another interpolation method using Voronoi diagrams recently. This paper outlines the au...

To fill a theory gap of Voronoi diagrams that there have been no reports of extended diagrams in spatial density so far. A new concept of spatial density Voronoi diagram was proposed. An important property was presented and proven. And a construction algorithm was presented. Spatial density can be used to indicate factors related to density such as conveyance and the traffic conditions. Some pr...

A discussion of reduced-order modeling for complex systems such as fluid flows is given to provide a context for the construction and application of reduced-order bases. Reviews of the POD (proper orthogonal decomposition) and CVT (centroidal Voronoi tessellation) approaches to reduced-order modeling are provided, including descriptions of POD and CVT reduced-order bases, their construction fro...

In this paper, we first develop a centroidal Voronoi tessellation (CVT) based surface segmentation algorithm using eigenfunctions of the Secondary Laplace operator (SLO). We then present a novel automatic polycube construction algorithm based on a generalized harmonic boundary-enhanced CVT (gHBECVT) by including the curve-skeleton information. Based on the constructed polycube, we generate qual...

This paper overviews the whole-body force control framework implemented on the iCub humanoid platform. This framework consists in a hierarchy of two tasks, where the highest priority task is a force control task, and the lowest one a postural task. The force task achieves the stabilization of a desired centroidal dynamics, i.e., a desired linear and angular momentum of the multi body system. Th...

In this paper, we study a finite-volume method for the numerical solution of a model fourth-order partial differential equation defined on a smooth surface. The discretization is done via a surface mesh consisting of piecewise planar triangles and its dual surface polygonal tessellation. We provide an error estimate for the approximate solution under the H1-norm on general regular meshes. Numer...

We present a novel clustering algorithm for polygonal meshes which approximates a Centroidal Voronoi Diagram construction. The clustering provides an efficient way to construct uniform tessellations, and therefore leads to uniform coarsening of polygonal meshes, when the output triangulation has many fewer elements than the input mesh. The mesh topology is also simplified by the clustering algo...