TR-Tf3 Perspective Conjugate (Isoconjugate)

The Perspective Conjugate of a point P with respect to a Reference Triangle ABC and a Perspective Center M is the perspective reflection of P in M.

Clarification

For each sideline of ABC, we consider the corresponding pair of vertices together with the traces Px (x=a,b,c) and Mx (x=a,b,c) of P and M. On that same sideline, we also have a vanishing point Vx (x=a,b,c), defined as the intersection of the sideline with the trilinear polar of M (TR-Tf1). Using this information, the point Rx, the perspective reflection of Px in Mx, can be determined using PR-Tf3. The three reflection points Rx (x=a,b,c) obtained in this way are the traces of a point R, which is the Perspective Conjugate of P.

Note: The Perspective Conjugate is functionally equivalent to the Isoconjugate in the setting of a reference triangle.

Construction

The following figure illustrates the construction.

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