A Minimalist’s Implementation of the 3-d Divide-and-Conquer Convex Hull Algorithm

نویسنده

  • Timothy M. Chan
چکیده

We give a simple interpretation and a simple implementation of the classical divide-andconquer algorithm for computing 3-d convex hulls (and in particular, 2-d Delaunay triangulations and Voronoi diagrams). The entire C++ code is under 100 lines long, requires no special data structures, and uses only 6n pointers for space.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Framework for Multi-Core Implementations of Divide and Conquer Algorithms and its Application to the Convex Hull Problem

We present a framework for multi-core implementations of divide and conquer algorithms and show its efficiency and ease of use by applying it to the fundamental geometric problem of computing the convex hull of a point set. We concentrate on the Quickhull algorithm introduced in [2]. In general the framework can easily be used for any D&C-algorithm. It is only required that the algorithm is imp...

متن کامل

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 ...

متن کامل

Convex Hull in Higher Dimensions 1 Introduction

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 sec...

متن کامل

The Design of Divide and Conquer Algorithms

The structure common to a class of divide and conquer algorithms is represented by a program scheme. A theorem is presented which relates the functionality of a divide and conquer algorithm to its structure and the functionalities of its subalgorithms. Several strategies for designing divide and conquer algorithms arise from this theorem and they are used to formally derive algorithms for sorti...

متن کامل

Divide and Conquer for Llyear Emecfed Time

Divide-and-conquer is one of the most frequently used methods for the design or” fast algorithms. The most common application of the technique involves breaking a problem of size N into two subproblems of size N/2, solving these subproblems, then doing work proportional to N to “marry” the partial answers into a solution for the entire problem; this scheme leads to algorithms of O(N log N) wors...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2003