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Math: Geometric Art: Problem 59. Right and Equilateral Triangles, Delaunay Triangulation. Trimaginator apps for iPad and iPhone

Geometry Art Problem 59, Right and Equilateral Triangles, Delaunay Triangulation. Trimaginator apps for iPad and iPhone

 

Trimaginator for iPad and iPhone by Paul Ollivier
Trimaginator is inspired by the triangulation invented by the mathematician Boris Delaunay in 1934. While the process behind is complicated, the image is reduced to its essentials and turned into a triangle mesh.

12 Rendering modes and Automatic Point Generation Algorithms: Classic Edge detection, Isoline levels full mapping, Isoline levels scan through 8 levels.



Delaunay Triangulation
A Delaunay triangulation for a set P of points in the plane is a triangulation such that no point in P is inside the circumcircle of any triangle in the triangulation. It can be shown that for all possible triangulations of P, a Delaunay triangulation maximizes the minimum angle of all angles of the triangles in the triangulation. Thus, a Delaunay triangulation tends to avoid skinny triangles.

Delaunay triangulation is a good application of the circumcircle (circle which passes through the three vertices of a triangle). 

See also:
Original problem 59

Original problem art 59 


 

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Last updated: Sep 5, 2014