Abstract
We present a multiresolution model for terrain surfaces which is able to handle large-scale global topographic data. It is based on a hierarchical decomposition of the sphere by a recursive bisection triangulation in geographic coordinates. Error indicators allow the representation of the data at various levels of detail and enable data compression by local omission of data values. The resulting adaptive hierarchical triangulation is stored using a bit code of the underlying binary tree and additionally, relative pointers which allow a selective tree traversal. This way, it is possible to work directly on the compressed data. We show that significant compression rates can be obtained already for small threshold values. In a visualization application, adaptive triangulations which consist of hundreds of thousands of shaded triangles are extracted and drawn at interactive rates.
Similar content being viewed by others
References
L. De Floriani, E. Puppo, and P. Magillo. “Geometric structures and algorithms for geographic information systems,” in J.R. Sack and J. Urrutia (Eds.), Handbook of Computational Geometry, 333–388, 1999.
M. Duchaineau, M. Wolinsky, D.E. Sigeti, M.C. Miller, C. Aldrich, and M.B. Mineev-Weinstein. “ROAMing terrain: Real-time optimally adapting meshes,” in Proc. Visualization '97, 81–88, IEEE Computer Society Press, 1997.
G.H. Dutton. “A hierarchical coordinate system for geoprocessing and cartography,” Lecture Notes in Earth Sciences 79, Springer, 1999.
W. Evans, D. Kirkpatrick, and G. Townsend. “Right-triangulated irregular networks,” Algorithmica, Vol. 30(2):264–286, 2001.
T. Gerstner. “Ein adaptives hierarchisches Verfahren zur Approximation und effizienten Visualisierung von Funktionen und seine Anwendung auf digitale 3–D Höhenmodelle,” Master's thesis, Institut für Informatik, TU München, 1995.
T. Gerstner. “Adaptive hierarchical methods for landscape representation and analysis,” in S. Hergarten, H. J. Neugebauer (Eds.), Process Modelling and Landform Evolution, 75–92, Lecture Notes in Earth Sciences 78, Springer, 1999.
T. Gerstner, M. Rumpf, and U. Weikard. “Error indicators for multilevel visualization and computing on nested grids,” Computers & Graphics, Vol. 24(3):363–373, 2000.
M. Griebel, and G. Zumbusch. “Parallel multigrid in an adaptive PDE solver based on hashing and space-filling curves,” Parallel Computing, Vol. 25:827–843, 1999.
M.H. Gross, O.G. Staadt, and R. Gatti. “Efficient triangular surface approximations using wavelets and quadtree data structures,” IEEE Trans. on Visualization and Computer Graphics, Vol. 2(2):130–143, 1996.
D.J. Hebert. “Cyclic interlaced quadtree algorithms for Quincunx multiresolution,” J. Algorithms, Vol. 27:97–129, 1998.
D.J. Hebert and H.-J. Kim. “Image encoding with triangulation wavelets,” in A.F. Laine, M.A. Unser, M.V. Wickerhauser (Eds.), Wavelet Applications in Signal and Image Processing III, 381–392, 1995.
P.S. Heckbert and M. Garland. Survey of Surface Approximation Algorithms, Technical Report CMU-CS-95–194, Department of Computer Science, Carnegie Mellon University, 1995.
M. Lee and H. Samet. “Navigating through triangle meshes implemented as linear quadtrees,” ACM Transactions on Graphics, Vol. 19(2):79–121, 2000.
P. Lindstrom, D. Koller, W. Ribarsky, L.F. Hodges, N. Faust, and G. Turner. “Real-time, continuous level of detail rendering of height fields,” Computer Graphics (Proc. SIGGRAPH '96), 109–118, 1996.
P. Lindstrom and V. Pascucci. “Visualization of large terrains made easy,” in Proc. IEEE Visualization '01, 363–370, IEEE Computer Society Press, 2001.
J. Maubach. “Local bisection refinement for n-simplicial grids generated by reflection,” SIAM J. Sci. Comput., Vol. 16:210–227, 1995.
W.F. Mitchell. “Adaptive refinement for arbitrary finite element spaces with hierarchical bases,” J. Comp. Appl. Math., Vol. 36:65–78, 1991.
M. Ohlberger and M. Rumpf. “Adaptive projection methods in multiresolutional scientific visualization,” IEEE Transactions on Visualization and Computer Graphics, Vol. 4(4):74–94,1998.
R. Pajarola. “Large scale terrain visualization using the restricted quadtree triangulation,” in Proc. IEEE Visualization '98, 19–24, IEEE Computer Society Press, 1998.
A. Paul and K. Dobler. “Adaptive realtime terrain triangulation,” in Proc. WSCG '97, University of West Bohemia, Plzen, Czech Republic, 1997.
E. Puppo and R. Scopigno. “Simplification, LOD and multiresolution principles and applications,” Eurographics '97 Tutorial Notes, Eurographics Association, 1997.
S. Röttger, W. Heidrich, P. Slussallek, and H.-P. Seidel. “Real-time generation of continuous levels of detail for height fields,” Proc. 6th Int. Conf. in Central Europe on Computer Graphics and Visualization, 315–322, 1998.
M.C. Rivara. “Algorithms for refining triangular grids suitable for adaptive and multigrid techniques,” International Journal for Numerical Methods in Engineering, Vol. 20:745–756, 1984.
H. Sagan. Space-filling Curves, Springer, 1994.
H. Samet. The Design and Analysis of Spatial Data Structures, Addison-Wesley, 1990.
D. Salomon. Data Compression, Springer, 1997.
W. Sierpiński. “Sur une nouvelle courbe continue qui remplit toute une aire plane,” Bull. Acad. Sci. de Cracovie, 462–478, 1912.
B. Von Herzen and A.H. Barr. “Accurate triangulations of deformed, intersecting surfaces,” Computer Graphics (Proc. SIGGRAPH '87), 103–110, 1987.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gerstner, T. Multiresolution Compression and Visualization of Global Topographic Data. GeoInformatica 7, 7–32 (2003). https://doi.org/10.1023/A:1022818126783
Issue Date:
DOI: https://doi.org/10.1023/A:1022818126783