Computational geometry: an introduction
Computational geometry: an introduction
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Fuzzy Sets and Systems - Special issue on fuzzy relations, part 1
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Modeling uncertain data with fuzzy B-splines
Fuzzy Sets and Systems
A New Approach to Incorporate Uncertainty in Terrain Modeling
GIScience '02 Proceedings of the Second International Conference on Geographic Information Science
Interval methods in knowledge representation
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
An application of the fuzzy theory in surface interpolation and surface deformation analysis
Fuzzy Sets and Systems
Multi-visibility maps of triangulated terrains
International Journal of Geographical Information Science
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The construction of inter-visibility models for a terrain is an important tool for environmental and animal studies. Efficient crisp algorithms are known to address this problem directly on a raster digital elevation map (DEM) of the study area. Randomness plays an important role: several factors like vegetation, height of the observer, presence of unmapped human artifacts, etc. cannot be modeled in advance into a traditional DEM model. We propose the use of fuzzy terrain models to incorporate uncertainty and unpredictable variability of the landscape. Accordingly, we propose a suitable definition of visibility to obtain intervisibility models. An algorithm that uses approximation of fuzzy numbers with a discrete family of intervals is proposed.The proposed model produces sound results and can be extended to model complex situations like triangulating a radio source using two directional receivers. All of these situations are difficult to manage with a precise stochastic model and are a frequent occurrence in animal behavior studies under field conditions. The proposed techniques have been implemented inside a user-friendly software package that may easily exchange data with the most common GISs. We report also some experimental results obtained using over artificial terrain under controlled noise and under-sampling conditions.