Convex hull optimization tutorial

  • What is convex hull trick?

    The convex hull trick is a technique (perhaps best classified as a data structure) used to determine efficiently, after preprocessing, which member of a set of linear functions in one variable attains an extremal value for a given value of the independent variable..

  • Convex Hull using Graham Scan

    1.
    1. Find the bottom-most point by comparing y coordinate of all points
      2. . 2.
    2. Consider the remaining n-1 points and sort them by polar angle in counterclockwise order around points[0]
      3. . 33 After sorting, check if two or more points have the same angle.
  • As it does, it stores a convex sequence of vertices on the stack, the ones that have not yet been identified as being within pockets.
    At each step, the algorithm follows a path along the polygon from the stack top to the next vertex that is not in one of the two pockets adjacent to the stack top.
Table of Contents. TutorialSolution - The Fair Nut and RectanglesProblems. We wish to solve problems that are of the following form:.

How to solve a convex hull problem for a planar point set?

Convex Hull by Divide-and-Conquer: As with sorting, there are many di erent approaches to solving the convex hull problem for a planar point set P

Next, we will consider another O(n log n) algorithm, which is based on divide-and-conquer

Is there a makeshift package for 3 dimensional convex hulls?

A makeshift package for computing three-dimensional convex hulls in the Wolfram Language has been written by Meeussen and Weisstein

In dimensions, the "gift wrapping" algorithm, which has complexity , where is the floor function , can be used (Skiena 1997, p

352)

Should convex hull vertices be sorted by x-coordinate?

It found the lowest point in the data set and then sorted points cyclically around this point

Sorting by x-coordinate seems to be a bit easier to implement, however

) Since we are working from left to right, it would be convenient if the convex hull vertices were also ordered from left to right


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