Breaklines in Coons surfaces over triangles for the use in terrain modelling

Authors:
Marco Hugentobler;Bernhard Schneider
Affiliations:
Department of Geography, University of Zurich, Zurich, Switzerland;Department of Geosciences, University of Basel, Bernoullistrasse 32, CH4056, Basel, Switzerland
Venue:
Computers & Geosciences
Year:
2005

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Abstract

The discipline of computer aided geometric design provides a number of surface interpolation techniques suitable for digitally specifying topographic surfaces, including Bezier and B-splines as well as Coons patches. The latter technique, rarely used in digital terrain modelling so far, is based on an intuitive concept. In a first step, a net of boundary curves is specified. In a second step, Coons patches are specified from these curves so that the resulting surface is globally zero- or first-order continuous. This paper introduces a modification to the triangular Coons patch method allowing the consideration and modelling of breaklines. The method leaves the boundary curves representing breaklines unchanged but alters the curves leading to breakline vertices. In order to abandon first-order continuity, it introduces left- and right-side surface normals at the breakline vertices and uses a special configuration of the cross-boundary derivatives. The results are visually and quantitatively assessed.