The input/output complexity of sorting and related problems
Communications of the ACM
I/O optimal isosurface extraction (extended abstract)
VIS '97 Proceedings of the 8th conference on Visualization '97
External-memory graph algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
I/O-efficient algorithms for contour-line extraction and planar graph blocking
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
External memory algorithms and data structures
External memory algorithms
An Efficient Multiversion Access Structure
IEEE Transactions on Knowledge and Data Engineering
Computing contour trees in all dimensions
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
External memory data structures
Handbook of massive data sets
Loops in Reeb Graphs of 2-Manifolds
Discrete & Computational Geometry
I/O-efficient batched union-find and its applications to terrain analysis
Proceedings of the twenty-second annual symposium on Computational geometry
TerraStream: from elevation data to watershed hierarchies
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
I/o-efficient efficient algorithms for computing contours on a terrain
Proceedings of the twenty-fourth annual symposium on Computational geometry
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A terrain M can be represented as a triangulation of the plane along with a height function associated with the vertices (and linearly interpolated within the edges and triangles) of M. We investigate the problem of answering contour queries on M: Given a height l and a triangle f of M that intersects the level set of M at height l, report the list of the edges of the connected component of this level set that intersect f, sorted in clockwise or counter-clockwise order. Contour queries are different from level-set queries in that only one contour (connected component of the level set) out of all those that may exist is expected to be reported. We present an I/O-efficient data structure of linear size that answers a contour query in O(logB N + T/B) I/Os, where N is the number of triangles in the terrain and T is the number of edges in the output contour. The data structure can be constructed using O(Sort(N)) I/Os.