Convex Hull in Higher Dimensions 1 Introduction
نویسندگان
چکیده
This lecture describes a data structure for representing convex polytopes and a divide and conquer algorithm for computing convex hull in 3 dimensions. Let S be a set of n points in . Convex hull of S (CH(S)) is the smallest convex polytope that contains all n points. Since the boundary of this polytope is planar, it can be efficiently represented by the data structure described in the next section (only true for 3D).
منابع مشابه
The Convex Hull of a Sample
1. The convex hull of a random sample may be considered as one possible analogue of the range of a one-dimensional sample. Recent work along this line has dealt with the expected number of vertices, faces, surface area and other quantities connected with the convex hull of n independently and identically distributed random points in the plane and in higher dimensions. See Renyi and Salanke [6] ...
متن کامل7. Acknowledgments 8. References 6. Concluding Remarks
Optimal algorithms for computing the minimum distance between two finite planar sets, " Proc. A fast algorithm for the planar convex hull problem, " internal manuscript, [25] B. K. Bhattacharya and G. T. Toussaint. " A time-and-storage efficient implementation of an optimal planar convex hull algorithm, " Divide and conquer for linear expected time, " Inform. A linear algorithm for finding the ...
متن کاملSweep Line Algorithm for Convex Hull Revisited
Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...
متن کاملOptimal Output-Sensitive Convex Hull Algorithms in Two and Three Dimensions
We present simple output-sensitive algorithms that construct the convex hull of a set of n points in two or three dimensions in worst-case optimal O (n log h) time and O(n) space, where h denotes the number of vertices of the convex hull.
متن کاملOn the Most Likely Convex Hull of Uncertain Points
Consider a set of d-dimensional points where the existence or the location of each point is determined by a probability distribution. The convex hull of this set is a random variable distributed over exponentially many choices. We are interested in finding the most likely convex hull, namely, the one with the maximum probability of occurrence. We investigate this problem under two natural model...
متن کامل