Geometry in the Real World

Geometry in the Real World: Las Vegas Strip, Southern Half and Delaunay Triangulation. iPad App: Trimaginator

Las Vegas Strip, Nevada and Delaunay Triangulation Art, Panorama

Las Vegas Strip, Southern Half by night..
 

Polygonal Art Illustration: Las Vegas
Las Vegas is a city in the United States, the most populous city in the state of Nevada. Las Vegas is an internationally renowned major resort city known primarily for gambling, shopping, fine dining and nightlife and is the leading financial and cultural center for Southern Nevada. The city bills itself as The Entertainment Capital of the World, and is famous for its mega casino–hotels and associated entertainment. A growing retirement and family city, Las Vegas is the 30th-most populous city in the United States. Source: Wikipedia: Las Vegas.

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.

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

Download on the App Store: Trimaginator ▲ - Paul Ollivier

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 Jan 29, 2015