Geometric Art

Empire State Building & Delaunay Triangulation. iPad App: Trimaginator

Empire State Building and Delaunay Triangulation Art


Polygonal Art Illustration: Empire State Building

The Empire State Building is a 102-story skyscraper located in Midtown Manhattan, New York City, on Fifth Avenue between West 33rd and 34th Streets. It has a roof height of 1,250 feet (380 m), and with its antenna spire included, it stands a total of 1,454 feet (443 m) high. The Empire State Building is currently the fourth-tallest completed skyscraper in the United States (after the One World Trade Center, the Willis Tower and Trump International Hotel and Tower, both in Chicago), and the 25th-tallest in the world (the tallest now is Burj Khalifa, located in Dubai).

The Empire State Building is generally thought of as an American cultural icon. It is designed in the distinctive Art Deco style and has been named as one of the Seven Wonders of the Modern World by the American Society of Civil Engineers. Source: Wikipedia: Empire State Building

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 Mar 13, 2015