Geometry in the Real World

Geometry in the Real World: Santorini, Greece and Delaunay Triangulation. iPad App: Trimaginator

Santorini, Greece and Delaunay Triangulation Art, Panorama

Polygonal Art Illustration: Santorini, Greece
Santorini is an island in the southern Aegean Sea, about 120 mi southeast from Greece's mainland. It is the largest island of a small, circular archipelago which bears the same name and is the remnant of a volcanic caldera. It forms the southernmost member of the Cyclades group of islands, with an area of approximately 28 sq mi and a 2011 census population of 15,550.

Santorini was named by the Latin Empire in the thirteenth century, and is a reference to Saint Irene, from the name of the old cathedral in the village of Perissa.

Santorini's primary industry is tourism, particularly in the summer months. It was ranked world's top island for 2011 in Travel+Leisure Magazine. Santorini was also named "the world's best island" by the BBC in 2011 Source: Wikipedia, Santorini.

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 | Santorini | Computational Geometry | Trimaginator for iPad | Delaunay Triangulation | Geometry for Kids | Software | Email | Post a comment | by Antonio Gutierrez
Last updated July 7, 2014