QG-Co2: Circumscribed Harmonic Conic
The Circumscribed Harmonic Conic is the projective transformation of the circumscribed circle of a square to the Reference Quadrigon.
See chapter QG-Tf1: QG-Projective Square Transformation.
This conic touches the sidelines of the projective circumscribed Quadrigon at the vertices of the Reference Quadrigon.
See picture below.
Construction:
Equations:
Equation QG-Co2 in 3 QA-Quadrigons in CT-notation:
- -2 r x y + q x z + p y z = 0
- r x y - 2 q x z + p y z = 0
- r x y + q x z - 2 p y z = 0
Equation QG-Co2 in 3 QL-Quadrigons in CT-notation:
- l2 x2 + l m x y + l n x z - m n y z = 0
- m2 y2 + l m x y - l n x z + m n y z = 0
- n2 z2 - l m x y + l n x z + m n y z = 0
Equation QG-Co2 in 3 QA-Quadrigons in DT-notation:
- q2 r2 x2 - 2 p2 r2 y2 + p2 q2 z2 = 0
- -2 q2 r2 x2 + p2 r2 y2 + p2 q2 z2 = 0
- q2 r2 x2 + p2 r2 y2 - 2 p2 q2 z2 = 0
Equation QG-Co2 in 3 QL-Quadrigons in DT-notation:
- x2 l2 - y2 m2 + z2 n2 = 0
- -x2 l2 + y2 m2 + z2 n2 = 0
- x2 l2 + y2 m2 - z2 n2 = 0
Properties: