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A counterexample to a diameter algorithm for convex polygons.

B K Bhattacharya¹, G T Toussaint

¹School of Computer Science, McGill University, Montreal, P.Q., Canada.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|August 27, 2011

Summary

This summary is machine-generated.

Snyder and Tang's algorithm for convex polygon diameter fails for specific cases. However, the diameter of any simple polygon can be found in linear time.

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Area of Science:

Computational Geometry
Algorithm Analysis

Background:

The diameter of a convex polygon is a fundamental problem in computational geometry.
Snyder and Tang recently proposed an algorithm for this problem.

Purpose of the Study:

To identify limitations of the Snyder and Tang algorithm.
To present an efficient method for computing the diameter of simple polygons.

Main Methods:

Analysis of a specific family of convex polygons.
Theoretical examination of polygon diameter computation.

Main Results:

A class of convex polygons was identified where the Snyder and Tang algorithm produces incorrect results.
Demonstration that the diameter of any simple n-vertex polygon is computable in O(n) time.

Conclusions:

The Snyder and Tang algorithm is not universally applicable for convex polygon diameter.
An O(n) time complexity for computing the diameter of arbitrary simple polygons is established.