https://github.com/d-e-s-o/delaunay-triangulation

Delaunay triangulation using an incremental insertion algorithm, implemented in JavaScript.
https://github.com/d-e-s-o/delaunay-triangulation

algorithm applet delaunay delaunay-triangulation javascript triangle

Last synced: 3 months ago
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Delaunay triangulation using an incremental insertion algorithm, implemented in JavaScript.

• Host: GitHub
• URL: https://github.com/d-e-s-o/delaunay-triangulation
• Owner: d-e-s-o
• Created: 2017-04-16T15:53:43.000Z (almost 8 years ago)
• Default Branch: master
• Last Pushed: 2024-10-21T15:28:38.000Z (4 months ago)
• Last Synced: 2024-10-22T02:23:59.777Z (4 months ago)
• Topics: algorithm, applet, delaunay, delaunay-triangulation, javascript, triangle
• Language: JavaScript
• Homepage:
• Size: 22.5 KB
• Stars: 1
• Watchers: 3
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
delaunay-triangulation

======================

This project provides the functionality for creating a [Delaunay

Triangulation][delaunay] of a given point set. It does so using an

incremental insertion algorithm, which means that it possible to insert

new points into the triangulated net at any time. The whole algorithm is

implemented for points in 3D space but the provided [visualization

applet][applet] works in the plane (i.e., with `z = 0`).

The algorithm is implemented (mostly) as proposed by Adrian Bowyer in

his paper ['Computing Dirichlet Tessellations'][bowyer] (1981).

The Algorithm

-------------

- an initial triangle is formed that *must* contain all points to be

  added in the future and comprises the initial root triangle of the net

- upon insertion of a new point the triangle that contains this point

  is searched in the net of triangles (there must always be one!) --

  this is done using the A*-search algorithm using the distance from

  the new point to the closest of each triangles forming points,

  i.e., the one with the minimum distance to this point, as the

  performance measure

- the found triangle is split into three by incorporation of the new

  point

- the newly created triangles are checked for the Delaunay condition:

  - the circumcircle of each triangle only contains the points in the

    triangle itself, none of its neighbors

- if this condition is violated, it will be fixed by flipping the

  edges of the two triangles under consideration

  - only if a violation was detected, the search for other violated

    triangles continues for neighbors that are farther away than the

    previous one

[delaunay]: https://en.wikipedia.org/wiki/Delaunay_triangulation

[applet]: https://d-e-s-o.github.io/delaunay-triangulation

[bowyer]: https://doi.org/10.1093/comjnl/24.2.162