Geometry in the Real World

White House & Delaunay Triangulation. iPad App: Trimaginator

White House and Delaunay Triangulation Art, Panorama


Polygonal Art Illustration: White House

The White House is the official residence and principal workplace of the President of the United States, located at 1600 Pennsylvania Avenue Northwest, Washington, D.C.. It has been the residence of every U.S. president since John Adams in 1800.

The house was designed by Irish-born James Hoban, and built between 1792 and 1800 of white-painted Aquia Creek sandstone in the Neoclassical style. Source: Wikipedia: White House.

Trimaginator for iPad 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).
 


 

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Last updated July 2, 2014