Since different good parametrizations are related themselves by line homographies, the definition is independent of the particular good parametrization. Since they are (via S) described by homographies they share with them the following fundamental properties:

[1] They preserve the

[2] They are distinguished in

[3] Involutive/non-involutive are completely determined by 2/3 points of the conic and their images on it.

[4] They can have no/one (the non-involutive)/or two fixed points.

[5] They can be extended to global homographies (or projectivities) of the projective plane.

Involutive homographies are examined in InvolutiveHomography.html . Here we continue with the non-involutive case.

The main characteristic of a conic homography (involutive or not) is its

In the image below we define a conic homography F by prescribing the images 1', 2', 3' of three points 1, 2, 3 of the conic. The homography axis (pink) is displayed and the intersection point P of lines 13', 1'3 is seen to be on this axis. F

The conic (c) and the homography axis (considered as a degenerated double-line-conic) generate a family (I) of conics. Further F can be extended to a projectivity F

ConicHomography.html

HomographyAxis.html

InvolutiveHomography.html

CrossRatio.html

GoodParametrization.html

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