94 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
Convex Hulls: Surface Mapping onto a Sphere
Writing an uncomplicated, robust, and scalable three-dimensional convex hull
algorithm is challenging and problematic. This includes, coplanar and collinear
issues, numerical accuracy, performance, and complexity trade-offs. While there
are a number of methods available for finding the convex hull based on
geometric calculations, such as, the distance between points, but do not
address the technical challenges when implementing a usable solution (e.g.,
numerical issues and degenerate cloud points). We explain some common algorithm
pitfalls and engineering modifications to overcome and solve these limitations.
We present a novel iterative method using support mapping and surface
projection to create an uncomplicated and robust 2d and 3d convex hull
algorithm
Fuzzy Clustering Using the Convex Hull as Geometrical Model
A new approach to fuzzy clustering is proposed in this paper. It aims to relax some constraints imposed by known algorithms using a generalized geometrical model for clusters that is based on the convex hull computation. A method is also proposed in order to determine suitable membership functions and hence to represent fuzzy clusters based on the adopted geometrical model. The convex hull is not only used at the end of clustering analysis for the geometric data interpretation but also used during the fuzzy data partitioning within an online sequential procedure in order to calculate the membership function. Consequently, a pure fuzzy clustering algorithm is obtained where clusters are fitted to the data distribution by means of the fuzzy membership of patterns to each cluster. The numerical results reported in the paper show the validity and the efficacy of the proposed approach with respect to other well-known clustering algorithms
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