Quickhull

About: Quickhull is a research topic. Over the lifetime, 56 publications have been published within this topic receiving 4860 citations.

The quickhull algorithm for convex hulls

Abstract: The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.

New Approach for Quantifying Process Feasibility: Convex and 1-D Quasi-Convex Regions

Abstract: Uncertainities in chemical plants come from numerous sources: internal like fluctu- atedalues of reaction constants and physical properties or external such as quality and flow rates of feedstreams. Accounting for uncertainty inarious stages of plant opera- tions was identified as one of the most important problems in chemical plant design and operations. A new approach proposed describes process's feasible region and a new metric for ealuating process flexibility based on the conex hull that is inscribed within the feasible region and determines itsolume based on Delaunay Triangulation. The two steps inoled are: 1. a series of simple optimization problems are soled to deter- mine points at the boundary of the feasible region; 2. gien the set of points at the boundary of the feasible region, the conex hull inscribed within the feasible region is determined. This is achieed by implementing the Quickhull algorithm, an incremental procedure for ealuating the conex hull, and then by computing a Delaunay Triangula- tion to determine theolume of the conex hull proiding a new metric for process flexibility. This approach not only proides another feasibility measure, but an accurate description of the feasible space of the process. It was applied to 1-D conex problems, and work is in progress to extend it to nonconex systems.

Randomized quickhull

Abstract: This paper contains a simple, randomized algorithm for constructing the convex hull of a set ofn points in the plane with expected running timeO(nlogh) whereh is the number of points on the convex hull.

Convex-Hull Algorithms: Implementation, Testing, and Experimentation

Abstract: From a broad perspective, we study issues related to implementation, testing, and experimentation in the context of geometric algorithms. Our focus is on the effect of quality of implementation on experimental results. More concisely, we study algorithms that compute convex hulls for a multiset of points in the plane. We introduce several improvements to the implementations of the studied algorithms: plane-sweep, torch, quickhull, and throw-away. With a new set of space-efficient implementations, the experimental results—in the integer-arithmetic setting—are different from those of earlier studies. From this, we conclude that utmost care is needed when doing experiments and when trying to draw solid conclusions upon them.