Volume-preserving interpolation of a smooth surface from polygon-related data |
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Authors: | Wolf-Dieter Rase |
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Institution: | (1) Federal Office for Building and Regional Planning (BBR) Am Michaelshof 8, 53177 Bonn, Germany (e-mail: rase@acm.org, rase@bbr.bund.de), DE |
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Abstract: | The interpolation of continuous surfaces from discrete points is supported by most GIS software packages. Some packages provide
additional options for the interpolation from 3D line objects, for example surface-specific lines, or contour lines digitized
from topographic maps. Demographic, social and economic data can also be used to construct and display smooth surfaces. The
variables are usually published as sums for polygonal units, such as the number of inhabitants in communities or counties.
In the case of point and line objects the geometric properties have to be maintained in the interpolated surface. For polygon-based
data the geometric properties of the polygon boundary and the volume should be preserved, avoiding redistribution of parts
of the volume to neighboring units during interpolation. The pycnophylactic interpolation method computes a continuous surface
from polygon-based data and simultaneously enforces volume preservation in the polygons. The original procedure using a regular
grid is extended to surface representations based on an irregular triangular network (TIN).
Received: 5 October 2000 / Accepted: 20 December 2000 |
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Keywords: | : Interpolation surface TIN cartography GIS regional planning |
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