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COMPGEOM
2010
ACM
15 years 6 months ago
3D Euler spirals for 3D curve completion
Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curves, which can be utilized for curv...
Gur Harary, Ayellet Tal
COMPGEOM
2010
ACM
15 years 6 months ago
Constructing Reeb graphs using cylinder maps
The Reeb graph of a scalar function represents the evolution of the topology of its level sets. In this video, we describe a near-optimal output-sensitive algorithm for computing ...
Harish Doraiswamy, Aneesh Sood, Vijay Natarajan
COMPGEOM
2010
ACM
15 years 6 months ago
Orthogonal range reporting: query lower bounds, optimal structures in 3-d, and higher-dimensional improvements
Orthogonal range reporting is the problem of storing a set of n points in d-dimensional space, such that the k points in an axis-orthogonal query box can be reported efficiently. ...
Peyman Afshani, Lars Arge, Kasper Dalgaard Larsen
COMPGEOM
2010
ACM
15 years 6 months ago
Adding one edge to planar graphs makes crossing number hard
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
Sergio Cabello, Bojan Mohar
COMPGEOM
2010
ACM
15 years 6 months ago
A dynamic data structure for approximate range searching
In this paper, we introduce a simple, randomized dynamic data structure for storing multidimensional point sets, called a quadtreap. This data structure is a randomized, balanced ...
David M. Mount, Eunhui Park
Discrete Geometry
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