Hierarchical Data Representations Based on Planar Voronoi Diagrams

Abstract

Multiresolution representation of high-dimensional scattered data is a fundamental problem in scientific visualization. This paper introduces a data hierarchy of Voronoi diagrams as a versatile solution. Given an arbitrary set of points in the plane, our goal is the construction of an approximation hierarchy using the Voronoi diagram as the essential building block. We have implemented two Voronoi diagram-based algorithms to demonstrate their usefulness for hierarchical scattered data approximation. The first algorithm uses a constant function to approximate the data within each Voronoi cell, and the second algorithm uses the Sibson interpolant [14].