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COMPGEOM
2010
ACM
13 years 10 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
13 years 10 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
13 years 10 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
13 years 10 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
13 years 10 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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