Simplifying Terrain Models and Measuring Terrain Model Accuracy

We describe a set of TIN simplification methods that enable the use of the triangulation hierarchy introduced by Kirkpatrick and modified by de Berg and Dobrindt. This triangulation hierarchy can be used to form a terrain model combining areas with varying levels of detail. One variant of the delete simplification method formed simplifications with accuracy close to the greedy method. We also investigated different variables that can be used to measure the accuracy of our simplified terrain models. Although the use of derivative statistics did not significantly alter our evaluation of the performance of our simplification methods, we recommend that any future comparisons should be aware of these alternative variables of surface characterization.

[1]  Charles L. Lawson,et al.  Transforming triangulations , 1972, Discret. Math..

[2]  Mark P. Kumler An Intensive Comparison of Triangulated Irregular Networks (TINs) and Digital Elevation Models (DEMs) , 1994 .

[3]  Leila De Floriani,et al.  Line-of-Sight Communication on Terrain Models , 1994, Int. J. Geogr. Inf. Sci..

[4]  V. Leitáo,et al.  Computer Graphics: Principles and Practice , 1995 .

[5]  James J. Little,et al.  Automatic extraction of Irregular Network digital terrain models , 1979, SIGGRAPH.

[6]  Z. T. Chen,et al.  Systematic selection of very important points (VIP) from digital terrain model for constructing triangular irregular network , 1987 .

[7]  M. Garland,et al.  Fast Polygonal Approximation of Terrains and Height Fields , 1998 .

[8]  E. Hammond,et al.  ANALYSIS OF PROPERTIES IN LAND FORM GEOGRAPHY: AN APPLICATION TO BROAD-SCALE LAND FORM MAPPING , 1964 .

[9]  David H. Douglas,et al.  ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE , 1973 .

[10]  Mark de Berg,et al.  Trekking in the Alps Without Freezing or Getting Tired , 1993, Algorithmica.

[11]  H. J. Arnold Introduction to the Practice of Statistics , 1990 .

[12]  N. M. Fenneman,et al.  Physiographic divisions of the United States , 1905 .

[13]  Mark de Berg,et al.  On levels of detail in terrains , 1995, SCG '95.

[14]  Farzin Mokhtarian,et al.  A Theory of Multi-Scale, Curvature and Torsion Based Shape Representation for Planar and Space Curves , 1990 .

[15]  Leila De Floriani,et al.  A hierarchical structure for surface approximation , 1984, Comput. Graph..

[16]  David G. Kirkpatrick,et al.  Optimal Search in Planar Subdivisions , 1983, SIAM J. Comput..

[17]  Leila De Floriani,et al.  A Hierarchical Triangle-Based Model for Terrain Description , 1992, Spatio-Temporal Reasoning.

[18]  Jay Lee,et al.  Comparison of existing methods for building triangular irregular network, models of terrain from grid digital elevation models , 1991, Int. J. Geogr. Inf. Sci..

[19]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[20]  S. Rippa,et al.  Data Dependent Triangulations for Piecewise Linear Interpolation , 1990 .

[21]  Lori Scarlatos,et al.  Hierarchical triangulation using terrain features , 1990, Proceedings of the First IEEE Conference on Visualization: Visualization `90.