9807

Paths inside a Polygon

This Demonstration illustrates an algorithm for finding the shortest path that stays inside a polygon and connects two given points. Aside from the start and finish, such a path must go from reflex vertex to reflex vertex; thus you start by first making the graph whose edges (shown in blue) are all the segments that stay inside the polygon and connect two such vertices (and the start and finish points). Then a standard shortest path algorithm yields the desired path. You can drag the start and finish points to new locations.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The algorithm presented here is relatively simple. A more sophisticated algorithm that is theoretically faster is called the funnel algorithm (see [1, 2]).
References
[1] B. Chazelle, "A Theorem on Polygon Cutting with Applications," in 23rd Annual Symposium on Foundations of Computer Science, 1982, pp. 339–349.
[2] D. T. Lee and F. P. Preparata, "Euclidean Shortest Paths in the Presence of Rectilinear Barriers," Networks, 14(3), 1984 pp. 393–410.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+