7,338 research outputs found
Incremental and Decremental Maintenance of Planar Width
We present an algorithm for maintaining the width of a planar point set
dynamically, as points are inserted or deleted. Our algorithm takes time
O(kn^epsilon) per update, where k is the amount of change the update causes in
the convex hull, n is the number of points in the set, and epsilon is any
arbitrarily small constant. For incremental or decremental update sequences,
the amortized time per update is O(n^epsilon).Comment: 7 pages; 2 figures. A preliminary version of this paper was presented
at the 10th ACM/SIAM Symp. Discrete Algorithms (SODA '99); this is the
journal version, and will appear in J. Algorithm
Algorithms for distance problems in planar complexes of global nonpositive curvature
CAT(0) metric spaces and hyperbolic spaces play an important role in
combinatorial and geometric group theory. In this paper, we present efficient
algorithms for distance problems in CAT(0) planar complexes. First of all, we
present an algorithm for answering single-point distance queries in a CAT(0)
planar complex. Namely, we show that for a CAT(0) planar complex K with n
vertices, one can construct in O(n^2 log n) time a data structure D of size
O(n^2) so that, given a point x in K, the shortest path gamma(x,y) between x
and the query point y can be computed in linear time. Our second algorithm
computes the convex hull of a finite set of points in a CAT(0) planar complex.
This algorithm is based on Toussaint's algorithm for computing the convex hull
of a finite set of points in a simple polygon and it constructs the convex hull
of a set of k points in O(n^2 log n + nk log k) time, using a data structure of
size O(n^2 + k)
Minimum Convex Partitions and Maximum Empty Polytopes
Let be a set of points in . A Steiner convex partition
is a tiling of with empty convex bodies. For every integer ,
we show that admits a Steiner convex partition with at most tiles. This bound is the best possible for points in general
position in the plane, and it is best possible apart from constant factors in
every fixed dimension . We also give the first constant-factor
approximation algorithm for computing a minimum Steiner convex partition of a
planar point set in general position. Establishing a tight lower bound for the
maximum volume of a tile in a Steiner convex partition of any points in the
unit cube is equivalent to a famous problem of Danzer and Rogers. It is
conjectured that the volume of the largest tile is .
Here we give a -approximation algorithm for computing the
maximum volume of an empty convex body amidst given points in the
-dimensional unit box .Comment: 16 pages, 4 figures; revised write-up with some running times
improve
Image based visual servoing using bitangent points applied to planar shape alignment
We present visual servoing strategies based on bitangents for aligning planar shapes. In order to acquire bitangents we use convex-hull of a curve. Bitangent points are employed in the construction of a feature vector to be used in visual control. Experimental results obtained on a 7 DOF Mitsubishi PA10 robot, verifies the proposed method
Convex Tours of Bounded Curvature
We consider the motion planning problem for a point constrained to move along
a smooth closed convex path of bounded curvature. The workspace of the moving
point is bounded by a convex polygon with m vertices, containing an obstacle in
a form of a simple polygon with vertices. We present an O(m+n) time
algorithm finding the path, going around the obstacle, whose curvature is the
smallest possible.Comment: 11 pages, 5 figures, abstract presented at European Symposium on
Algorithms 199
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