Geometry in the Real World

Geometry in the Real World: Washington Monument and Delaunay Triangulation. iPad App: Trimaginator

Washington Monument and Delaunay Triangulation Art, Panorama


Polygonal Art Illustration: Washington Monument

The Washington Monument is an obelisk on the National Mall in Washington, D.C., built to commemorate George Washington, once commander-in-chief of the early Continental Army and the first American president. The monument, made of marble, granite, and bluestone gneiss, is both the world's tallest stone structure and the world's tallest obelisk, standing 555 feet 5 1⁄8 inches tall. Source: Wikipedia, Washington Monument.

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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Home | Geometry | Geometric Art | Real World | Washington D.C. | Computational Geometry | Trimaginator for iPad | Delaunay Triangulation | Geometry for Kids | Software | Email | Post a comment | by Antonio Gutierrez
Last updated July 7, 2014