Voronoi図を用いた重心座標の拡張とその多次元データ補間への応用

抄録

The Voronoi diagram is useful for the interpolation of unstructured data in a multidimensional space, because it defines the neighbor relations among the data sites, and thus defines weights necessary for the interpolation. The previously known weight system with the highest continuity is the Sibson coordinate system. It gives an interpolant with C^1 continuity except at the data sites. However, that continuity is not satisfactory for many applications. This paper presents a new framework for constructing coordinate systems that have higher continuity than the Sibson coordinate system.