delaunaysimple

Intro

The simplest Delaunay Triangulation (DT) algorithm consists of encasing the simplex in a circle/sphere of that dimension (circle in 2D, sphere in 3D, ...) and rejecting the simplex if another point in the tessellation is within the generalized circle.

These algorithms are not practical because of their complexity.
In 2D DT is
and in 3D DT is
...

These algorithms work on the whole set of points at a time.

Source

Files

Doxygen

Simplest DT Algorithm in 2D

There are n points. Refer to the points by integer indexes.
Let x be the stack of triangles

function EvaluateTriangle(i,j,k)

Find the circle c through i,j,k
for w=0..n-1   where

If w is inside c

Reject the triangle i,j,k and exit function.

Accept the triangle i,j,k and push it onto x.

function main()

for i=0..n-3

for j=i+1..n-2

for k=j+1..n-1

EvaluateTriangle(i,j,k)

References

1. O'Rourke, Joseph(1984). Computational geometry in C. ISBN 0-521-445922

Design Algorithm

TODO

• Merge Delaynay3D which is miss spelt.
• Redocument and recode.
• Come up with a universal tessellation 2D data structure.