Abstract
In this paper, we present a model based on a collection of nested horizons to describe the visibility of a terrain with respect to a viewpoint. We introduce first a formalization of mathematical and digital terrain models, and some background notions for visibility problems on terrains. Then, we define horizons and shadows on a polyhedral terrain, and introduce a few horizon-based visibility maps of a terrain. Finally, we present two algorithms for building the nested horizons on a polyhedral terrain. An application to the solution of point-to-point visibility queries are briefly discussed.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
M.Atallah: Dynamic computational geometry. Proceedings 24th Symposium on Foundations of Computer Science, 1989, pp.92–99.
R. Cole, M.Sharir: Visibility problems for polyedral terrains. Technical Report 32, Courant Institute, New York University, 1986.
S.Cormack, C.M.Gold: Spatially ordered networks and topographic reconstruction. Int. J. GIS, vol.1, no.2, pp.137–148.
L.De Floriani: A pyramidal data structure for triangle-based surface description. IEEE Computer Graphics, March 1989, pp. 67–77.
L.De Floriani, B.Falcidieno, G.Nagy, C.Pienovi: On sorting triangles in a Delaunay tesselation. Algorithmica, Springer Verlag, 1991, N.6, pp.522–532.
L.De Floriani, E.Puppo: A hierarchical triangle-based model for terrain description. Theories and Methods of Spatio-Temporal Reasoning in Geometric Space, Springer Verlag, September 1992, pp. 236–251.
L.De Floriani, P.Magilio: Computing the horizon of a point on a polyhedral terrain. Submitted for publication, 1993.
L.De Floriani, P.Magillo: Computing point visibility on a terrain based on a nested horizon structure. Submitted for publication, 1993.
D.J.Foley, A.Van Dam, S.K.Feiner, J.F.Hughes: Computer Graphics: Principles and Practice. Addison Wesley, 1991.
C.M.Gold, U.M.Maydell: Triangulation and ordering in computer cartography. Proceedings, Canadian Cartographic Association's Third Annual Meeting, Vancouver, June 1978, pp. 69–81.
C.M.Gold: Spatial ordering of Voronoi networks and their use in terrain data base management. Proceedings, Auto-Carto 8, Baltimore, March 1987, pp. 185–194.
M.F.Goodchild, J.Lee: Coverage problems and visibility regions on topographic surfaces. Annals of Operation Research, 1989, 20, pp.175–186.
J.Hershberger: Finding the upper envelope of n line segments in O (n log n) time. Information Processing Letters, 33, 1989, pp.169–174.
J.Lee: Analyses of visibility sites on topographic surfaces. Int. J. of Geographical Information Systems, 1991, vol.5, n.4, pp.413–429.
M.McKenna: Worst case optimal hidden surface removal. ACM Trans. on Graphics, 1987, n.6, pp.19–28.
G. Nagy: Terrain visibility. Technical Report, Rensselaer Polytechnic Institute, 1990.
G.Nagy, N.C.Narendra, M.Sharir: Reconstruction of geographic terrains from horizon locations I: the 1-D case. In preparation, 1993.
G.Nagy, N.C.Narendra, M.Sharir: Reconstruction of geographic terrains from horizon locations II: the 2-D case. In preparation, 1993.
F.P.Preparata, M.I.Shamos: Computational Geometry: An Introduction. Springer Verlag, NY, 1985.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
De Floriani, L., Magillo, P. (1993). Computing visibility maps on a digital terrain model. In: Frank, A.U., Campari, I. (eds) Spatial Information Theory A Theoretical Basis for GIS. COSIT 1993. Lecture Notes in Computer Science, vol 716. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57207-4_17
Download citation
DOI: https://doi.org/10.1007/3-540-57207-4_17
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57207-7
Online ISBN: 978-3-540-47966-6
eBook Packages: Springer Book Archive