Geometric Art: Orthocenter of a Triangle, Altitudes, Delaunay Triangulation

Geometric Art: Orthocenter of a Triangle, Altitudes, Delaunay Triangulation


Orthocenter
The orthocenter of a triangle is the point of intersection of the three altitudes.

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).

 

Orthocenter of a Triangle in Motion
Click on the figure below.

 

Selected Topics

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Last updated Nov 22, 2014