Line voronoi diagram based interpolation and application to digital terrain modelling

Local coordinates based on the Voronoi diagram are used in natural neighbour interpolation to quantify the "neighbourliness" of data sites. In an earlier paper, we have extended the natural neighbour or stolen area interpolation technique from ordinary Voronoi diagrams to Voronoi diagrams for sets of points and line segments, by providing direct vectorial formulas for the first order and second order derivatives for the stolen area. This generalization allows one to model linear discontinuities, that are not modelable through current interpolation techniques. In this paper, we recall the continuity and differentiation properties of these local coordinates and natural neighbour interpolation, and we present their application to digital terrain modelling. In our case, the data sites can be either points or oriented line segments. We use this natural neighbour interpolation in order to interpolate elevations from the neighbouring data sites, and construct a digital terrain mode...

• Type: Conference
• Year: 2001
• Where: CCCG
• Authors: Francois Anton, Darka Mioc, Christopher M. Gold
• Keywords: CCCG 2001, CCCG 2007, Interpolation Technique, Line Segment, Natural Neighbour Interpolation