178 research outputs found
Finding Convex Hulls Using Quickhull on the GPU
We present a convex hull algorithm that is accelerated on commodity graphics
hardware. We analyze and identify the hurdles of writing a recursive divide and
conquer algorithm on the GPU and divise a framework for representing this class
of problems. Our framework transforms the recursive splitting step into a
permutation step that is well-suited for graphics hardware. Our convex hull
algorithm of choice is Quickhull. Our parallel Quickhull implementation (for
both 2D and 3D cases) achieves an order of magnitude speedup over standard
computational geometry libraries.Comment: 11 page
Improved Incremental Randomized Delaunay Triangulation
We propose a new data structure to compute the Delaunay triangulation of a
set of points in the plane. It combines good worst case complexity, fast
behavior on real data, and small memory occupation.
The location structure is organized into several levels. The lowest level
just consists of the triangulation, then each level contains the triangulation
of a small sample of the levels below. Point location is done by marching in a
triangulation to determine the nearest neighbor of the query at that level,
then the march restarts from that neighbor at the level below. Using a small
sample (3%) allows a small memory occupation; the march and the use of the
nearest neighbor to change levels quickly locate the query.Comment: 19 pages, 7 figures Proc. 14th Annu. ACM Sympos. Comput. Geom.,
106--115, 199
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