# Peeling Digital Potatoes

The potato-peeling problem (also known as convex skull) is a fundamental computational geometry problem and the fastest algorithm to date runs in O(n^8) time for a polygon with n vertices that may have holes. In this paper, we consider a digital version of the problem. A set K ⊂Z^2 is digital convex if conv(K) ∩Z^2 = K, where conv(K) denotes the convex hull of K. Given a set S of n lattice points, we present polynomial time algorithms to the problems of finding the largest digital convex subset K of S (digital potato-peeling problem) and the largest union of two digital convex subsets of S. The two algorithms take roughly O(n^3) and O(n^9) time, respectively. We also show that those algorithms provide an approximation to the continuous versions.

• 6 publications
• 15 publications
• 11 publications
research
01/15/2019

### Efficient Algorithms to Test Digital Convexity

A set S ⊂Z^d is digital convex if conv(S) ∩Z^d = S, where conv(S) denote...
research
03/08/2021

### Digital Convex + Unimodular Mapping =8-Connected (All Points but One 4-Connected)

In two dimensional digital geometry, two lattice points are 4-connected ...
research
11/15/2022

### About the Reconstruction of Convex Lattice Sets from One or Two X-rays

We consider a class of problems of Discrete Tomography which has been de...
research
12/22/2022

### Natural Way of Solving a Convex Hull Problem

In this article, a new solution for the convex hull problem has been pre...
research
07/24/2020

### Largest triangles in a polygon

We study the problem of finding maximum-area triangles that can be inscr...
research
10/16/2019

### Some Geometric Applications of Anti-Chains

We present an algorithmic framework for computing anti-chains of maximum...
research
07/02/2018

### Approximate Convex Intersection Detection with Applications to Width and Minkowski Sums

Approximation problems involving a single convex body in d-dimensional s...