Results 11  20
of
2,408
Rectilinear Geodesics in 3Space (Extended Abstract)
 In 11th Symp. Computational Geometry
, 1995
"... ) Joonsoo Choi CheeKeng Yap Courant Institute of Mathematical Sciences New York University 251, Mercer Street New York, NY 10012 Abstract Let B be any finite set of pairwisedisjoint, axesparallel boxes in Euclidean 3space. Our main theorem is that for any two points s; t 62 [B, there exists ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
a shortest rectilinear Bavoiding path from s to t that is monotone along at least one of the axes. The key concept in the proof is an appropriate notion of pyramids. Exploiting this result algorithmically, we obtain: a L1 shortest distance from a query point to a fixed source point can be computed
OutputSensitive Methods for Rectilinear Hidden Surface Removal
, 1993
"... We present an algorithm for the hiddensurface elimination problem for rectangles, which is also known as window rendering. The time complexity of our algorithm is dependent on both the number of input rectangles, n, and on the size of the output, k. Our algorithm obtains a tradeoff between these t ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
We present an algorithm for the hiddensurface elimination problem for rectangles, which is also known as window rendering. The time complexity of our algorithm is dependent on both the number of input rectangles, n, and on the size of the output, k. Our algorithm obtains a tradeoff between these two components, in that its running time is O(r(n 1 1=r k)), where 1 r log n is a tunable parameter. By using this method while adjusting the parameter r "on the fly" one can achieve a running time that is O(n log n k(log n= log(1 k=n))). Note that when k is \Theta(n), this achieves an O(n log n) running time, and when k is \Theta(n 1 ffl ) for any positive constant ffl, then this achieves an O(k) running time, both of which are optimal. A preliminary announcement of this research is to appear at the 17th International Colloquium on Automata, Languages, and Programming. Part of this research was carried out while the authors were visiting Princeton University for the DIMACS ...
Biorthogonal wavelets for subdivision volumes
 In: Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications
, 2002
"... Figure 1: Volume subdivision, manipulation, and fitting. A lattice (top left) is recursively subdivided and reshaped at the fourth subdivision level. This shape is lowpass filtered by removing fineresolution wavelet coefficients (bottom right). We present a biorthogonal wavelet construction based ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Figure 1: Volume subdivision, manipulation, and fitting. A lattice (top left) is recursively subdivided and reshaped at the fourth subdivision level. This shape is lowpass filtered by removing fineresolution wavelet coefficients (bottom right). We present a biorthogonal wavelet construction
AN OPTIMAL DATA STRUCTURE FOR SHORTEST RECTILINEAR PATH QUERIES IN A SIMPLE RECTILINEAR POLYGON
 INTERNATIONAL JOURNAL OF COMPUTATIONAL GEOMETRY & APPLICATIONS
, 1993
"... We present a data structure that allows to preprocess a rectilinear polygon with n vertices such that, for any two query points, the shortest path in the rectilinear link or L1metric can be reported in time O(log n + k) where k is the link length of the shortest path. If only the distance is of in ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
We present a data structure that allows to preprocess a rectilinear polygon with n vertices such that, for any two query points, the shortest path in the rectilinear link or L1metric can be reported in time O(log n + k) where k is the link length of the shortest path. If only the distance
Subdivision Schemes for Thin Plate Splines
, 1997
"... Thin plate splines are a well known entity of geometric design. They are defined as the minimizer of a variational problem whose differential operators approximate a simple notion of bending energy. Therefore, thin plate splines approximate surfaces with minimal bending energy and they are widely ..."
Abstract

Cited by 20 (2 self)
 Add to MetaCart
functions. This paper presents a novel approach for defining and computing thin plate splines using subdivision methods. We present two methods for the construction of thin plate splines based on subdivision: A globally supported subdivision scheme which exactly minimizes the energy functional as well
A Polynomial Time Approximation Scheme for the Symmetric Rectilinear Steiner Arborescence Problem
, 2002
"... The Symmetric Rectilinear Steiner Arborescence (SRStA) problem is defined as follows: given a set of terminals in the positive quadrant of the plane, connect them using horizontal and vertical lines such that each terminal can be reached from the origin via a ymonotone path and the total length o ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
The Symmetric Rectilinear Steiner Arborescence (SRStA) problem is defined as follows: given a set of terminals in the positive quadrant of the plane, connect them using horizontal and vertical lines such that each terminal can be reached from the origin via a ymonotone path and the total length
Image Segmentation by Directed Region Subdivision
 in Proc. IEEE Int. Conf. on Image Proc
, 1994
"... In this paper, an image segmentation method based on directed image region partitioning is proposed. The method consists of two separate stages: a splitting phase followed by a merging phase. The splitting phase starts with an initial coarse triangulation and employs the incremental Delaunay triangu ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
In this paper, an image segmentation method based on directed image region partitioning is proposed. The method consists of two separate stages: a splitting phase followed by a merging phase. The splitting phase starts with an initial coarse triangulation and employs the incremental Delaunay triangulation as a directed image region splitting technique. The triangulation process is accomplished by adding points as vertices one by one into the triangulation. A topdown point selection strategy is proposed for selecting these points in the image domain of greyvalue and color images. The merging phase coalesces the oversegmentation, generated by the splitting phase, into homogeneous image regions. Because images might be negatively affected by changes in intensity due to shading or surface orientation change, we propose homogeneity criteria which are robust to intensity changes caused by these phenomena for both greyvalue and color images. Performance of the image segmentation method has...
Binary space partitions of orthogonal subdivisions
 IN PROCEEDINGS OF THE 2004 ACM SYMPOSIUM ON COMPUTATIONAL GEOMETRY
, 2004
"... We consider the problem of constructing binary space partitions (BSPs) for orthogonal subdivisions (space filling packings of boxes) in dspace. We show that a subdivision with n boxes can be refined into a BSP of size O(n d+13), for all ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We consider the problem of constructing binary space partitions (BSPs) for orthogonal subdivisions (space filling packings of boxes) in dspace. We show that a subdivision with n boxes can be refined into a BSP of size O(n d+13), for all
PROXIMITY PROBLEMS FOR POINTS ON A RECTILINEAR PLANE WITH RECTANGULAR OBSTACLES
, 1993
"... We consider the following four problems for a set S of k points on a plane, equipped with the rectilinear metric and containing a set R of n disjoint rectangular obstacles (so that distance is measured by a shortest rectilinear path avoiding obstacles in R): (a) nd a closest pair of points in S, (b) ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We consider the following four problems for a set S of k points on a plane, equipped with the rectilinear metric and containing a set R of n disjoint rectangular obstacles (so that distance is measured by a shortest rectilinear path avoiding obstacles in R): (a) nd a closest pair of points in S, (b
Results 11  20
of
2,408