Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
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
Contour trees and small seed sets for isosurface traversal
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
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: dealing with massive data
ACM Computing Surveys (CSUR)
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
A Generic Approach to Bulk Loading Multidimensional Index Structures
VLDB '97 Proceedings of the 23rd International Conference on Very Large Data Bases
I/O-efficient topological sorting of planar DAGs
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
External memory data structures
Handbook of massive data sets
I/O-efficient batched union-find and its applications to terrain analysis
Proceedings of the twenty-second annual symposium on Computational geometry
Streaming computation of Delaunay triangulations
ACM SIGGRAPH 2006 Papers
TerraStream: from elevation data to watershed hierarchies
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
I/O-efficient contour queries on terrains
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Simplifying massive contour maps
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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A terrain M is the graph of a bivariate function. We assume that M is represented as a triangulated surface with N vertices. A contour (or isoline) of M is a connected component of a level set of M. Generically, each contour is a closed polygonal curve; at "critical" levels these curves may touch each other or collapse to a point. We present I/O efficient algorithms for the following two problems related to computing contours of M: (i) Given a sequence l1 ls of real numbers, we present an I/O-optimal algorithm that reports all contours of M at heights l1 , ... , ls using O(sort(N) + T/B) I/Os, where T is the total number edges in the output contours, B is the "block size," and sort(N) is the number of I/Os needed to sort N elements. The algorithm uses O(N/B) disk blocks. Each contour is generated individually with its composing segments sorted in clockwise or counterclockwise order. Moreover, our algorithm generates information on how the contours are nested. (ii) We can preprocess M, using O(sort(N)) I/Os, into a linear-size data structure so that all contours at a given height can be reported using O(logB N + T/B) I/Os, where T is the output size. Each contour is generated individually with its composing segments sorted in clockwise or counterclockwise order.