3,875 research outputs found
Maximal Area Triangles in a Convex Polygon
The widely known linear time algorithm for computing the maximum area
triangle in a convex polygon was found incorrect recently by Keikha et.
al.(arXiv:1705.11035). We present an alternative algorithm in this paper.
Comparing to the only previously known correct solution, ours is much simpler
and more efficient. More importantly, our new approach is powerful in solving
related problems
Gap Processing for Adaptive Maximal Poisson-Disk Sampling
In this paper, we study the generation of maximal Poisson-disk sets with
varying radii. First, we present a geometric analysis of gaps in such disk
sets. This analysis is the basis for maximal and adaptive sampling in Euclidean
space and on manifolds. Second, we propose efficient algorithms and data
structures to detect gaps and update gaps when disks are inserted, deleted,
moved, or have their radius changed. We build on the concepts of the regular
triangulation and the power diagram. Third, we will show how our analysis can
make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201
Toric surface codes and Minkowski length of polygons
In this paper we prove new lower bounds for the minimum distance of a toric
surface code defined by a convex lattice polygon P. The bounds involve a
geometric invariant L(P), called the full Minkowski length of P which can be
easily computed for any given P.Comment: 18 pages, 9 figure
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