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 model. We present an example of the use of the natural neighbour interpolation technique based on the Voronoi diagram for a set of points and oriented line segments for digital terrain modelling. The applications of this extended interpolation technique are shown for the modelling of linear vertical faults, dams or bridges. This research brings novelty in the modelling of topographic artifacts represented by line segments (e.g. thalwegs, crests, faults), because in the natural neghbour interpolation technique that we are using, line segments are data objects that can have an elevation (in fact an elevation for each oriented line segment).
Keyword: technology,reconstruction,digital,triangulation,GIS modelling