Geometry in the Real World

Geometry in the Real World: The Times Square and Delaunay Triangulation. iPad App: Trimaginator

Times Square and Delaunay Triangulation Art, Panorama


Polygonal Art Illustration: Times Square

Times Square is a major commercial intersection and a neighborhood in Midtown Manhattan, New York City, at the junction of Broadway and Seventh Avenue and stretching from West 42nd to West 47th Streets. According to Travel + Leisure magazine's October 2011 survey, Times Square is the world's most visited tourist attraction, hosting over 39 million visitors annually. Approximately 330,000 people pass through Times Square daily, many of whom are either tourists or people working in the area. Source: Wikipedia: Times Square.

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.

10 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 5, 2014