SIAM Journal on Computing
Shortest paths on a polyhedron
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Multiresolution surface modeling based on hierarchical triangulation
Computer Vision and Image Understanding
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Surface simplification using quadric error metrics
Proceedings of the 24th annual conference on Computer graphics and interactive techniques
A new algorithm for computing shortest paths in weighted planar subdivisions (extended abstract)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating weighted shortest paths on polyhedral surfaces
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Approximating Shortest Paths on a Nonconvex Polyhedron
SIAM Journal on Computing
GMP '00 Proceedings of the Geometric Modeling and Processing 2000
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
An efficient and scalable approach to CNN queries in a road network
VLDB '05 Proceedings of the 31st international conference on Very large data bases
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Query processing in spatial network databases
VLDB '03 Proceedings of the 29th international conference on Very large data bases - Volume 29
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Scalable network distance browsing in spatial databases
Proceedings of the 2008 ACM SIGMOD international conference on Management of data
A multi-resolution surface distance model for k-NN query processing
The VLDB Journal — The International Journal on Very Large Data Bases
Indexing land surface for efficient kNN query
Proceedings of the VLDB Endowment
Continuous monitoring of nearest neighbors on land surface
Proceedings of the VLDB Endowment
Expansion-Based algorithms for finding single pair shortest path on surface
W2GIS'04 Proceedings of the 4th international conference on Web and Wireless Geographical Information Systems
Monochromatic and bichromatic reverse nearest neighbor queries on land surfaces
Proceedings of the 21st ACM international conference on Information and knowledge management
The exact distance to destination in undirected world
The VLDB Journal — The International Journal on Very Large Data Bases
A framework of traveling companion discovery on trajectory data streams
ACM Transactions on Intelligent Systems and Technology (TIST) - Special Section on Intelligent Mobile Knowledge Discovery and Management Systems and Special Issue on Social Web Mining
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Finding shortest paths is a fundamental operator in spatial databases. Recently, terrain datasets have attracted a lot of attention from both industry and academia. There are some interesting issues to be studied in terrain datasets which cannot be found in a traditional two-dimensional space. In this paper, we study one of the issues called a slope constraint which exists in terrain datasets. In this paper, we propose a problem of finding shortest paths with the slope constraint. Then, we show that this new problem is more general than the traditional problem of finding shortest paths without considering the slope constraint. Since finding shortest paths with the slope constraint is costly, we propose a new framework called surface simplification so that we can compute shortest paths with the slope constraint efficiently. Under this framework, the surface is "simplified" such that the complexity of finding shortest paths on this simplified surface is lower. We conducted experiments to show that the surface simplification is very efficient and effective not only for the new problem with the slope constraint but also the traditional problem without the slope constraint.