TR-Tf1 Trilinear Polar

The Trilinear Polar of M with respect to a reference triangle ABC is the perspectrix of the Cevian triangle of M and ABC. It is a transformation that maps a point, in the context of a triangle, to a line.

From a perspectival viewpoint, the trilinear polar is the line at infinity generated by the perspectivities arising on each sideline of the triangle. For each sideline, the corresponding pair of vertices, together with the trace Mx (x=a,b,c) of M on that sideline — functioning as a perspective midpoint — determine a perspective scale with an associated vanishing point Vx. The three vanishing points Vx (x=a,b,c) obtained according to (PR-Tf1) are collinear, and their common line is the trilinear polar of M.

Construction

The following figure illustrates the construction.

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