Abstract
The standard method of building compact triangulated surface approximations to terrain surfaces (TINs) from dense digital elevation models (DEMs) adds points to an initial sparse triangulation or removes points from a dense initial mesh. Typically, in each triangle in the current TIN, the worst fitting point, in terms of vertical distance, is selected. The order of insertion of the points is determined by the magnitude of the maximum vertical difference. This measure produces triangulations that minimize the maximum vertical distance between the TIN and the source DEM. Other approximation criteria are often used, however, including the root-mean-squared error or the mean absolute error, both for the vertical difference and normal difference, i.e., the distance in the direction of the normal to the triangular approximation. For these approximation criteria, we still select the worst fit point, but determine the insertion order by various sums of errors over the triangle. Experiments show that using these better evaluation measures significantly reduces the size of the TIN for a given approximation error.
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Z.-T. Chen and J. Armando Guevara. “Systematic selection of very important points (VIP) from digital terrain model for constructing triangular irregular networks,” in N. Chrisman (Ed.), Proc. of Auto-Carto 8 (Eighth Intl. Symp. on Computer-Assisted Cartography), 50–56, American Congress of Surveying and Mapping: Baltimore, MD, 1987.
D.H. Douglas and T.K. Peucker. “Algorithms for the reduction of the number of points required to represent a digitized line or its caricature,” The Canadian Cartographer, Vol. 10(2):112–122, 1973.
N.D. and S. Rippa. “Data-dependent triangulations for scattered data interpolation and finite element approximation,” Applied Numer. Math., Vol. 12:89–105, 1993.
R.J. Fowler and J.J. Little. “An automatic method for the construction of irregular network digital terrain models,” in Proceedings of SIGGRAPH '79, 199–207, Chicago, Illinois, August 1979.
M. Garland and P.S. Heckbert. Fast polygonal approximation of terrains and height fields. Technical Report CMU-CS-95–181, Carnegie Mellon U., September 1995.
M. Heller. “Triangulation algorithms for adaptive terrain modeling,” in Proceedings of the 4th International Symposium of Spatial Data Handling, 163–174, 1990.
P.S. Heckbert and M. Garland. Survey of polygonal simplification algorithms. Technical report, CMU, 1997.
B. Junger and J. Snoeyink. “Importance measures for TIN simplification by parallel decimation,” in International Symposium on Spatial Data Handling '98, 637–646, 1998.
M.P. Kumler. “An intensive comparison of triangulated irregular networks (TINs) and digital elevation models (DEMs),” Cartographica, Vol. 31(2):1–48, 1994.
D. Lischinski. “Incremental Delaunay triangulation,” in P. Heckbert (Ed.), Graphics Gems IV. Academic Press, 1994.
J.J. Little and P. Shi. “Structural lines for triangulations of terrain,” IEEE Workshop on Applications of Computer Vision, 1998.
J.J. Little and P. Shi. “Structural lines, TINs, and DEMs,” Algorithmica, Vol. 30(2):243–263, 2001.
T.K. Peucker, R.J. Fowler, J.J. Little, and D.M. Mark. “The triangulated irregular network,” in Proc. of the Digital Terrain Models Symp., 516–532, St. Louis, MO, 1978.
M.F. Polis and D.M. McKeown. “Iterative TIN generation from digital elevation models,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition, 1992, 787–790, 1992.
F. Schmitt and X. Chen. “Vision-based construction of CAD models from range images,” in Proc. 4th International Conference on Computer Vision, 129–136, 1993.
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Little, J.J., Shi, P. Ordering Points for Incremental TIN Construction from DEMs. GeoInformatica 7, 33–53 (2003). https://doi.org/10.1023/A:1022870110853
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DOI: https://doi.org/10.1023/A:1022870110853