Geometry in the Real World

Geometry in the Real World: The Golden Gate Bridge and Delaunay Triangulation. iPad App: Trimaginator

Golden Gate Bridge and Delaunay Triangulation Art, Panorama


Polygonal Art Illustration: Golden Gate Bridge

The Golden Gate Bridge is a suspension bridge spanning the Golden Gate strait, the mile-wide, three-mile-long channel between San Francisco Bay and the Pacific Ocean. The structure links the U.S. city of San Francisco, on the northern tip of the San Francisco Peninsula, to Marin County. The bridge is one of the most internationally recognized symbols of San Francisco, California, and the United States. It has been declared one of the Wonders of the Modern World by the American Society of Civil Engineers. Source: Wikipedia: Golden Gate Bridge.

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