Geodesic
A Quadratic Transformation Based on a Straight Line and a Conic
Journal for geometry and graphics, Tome 6 (2002) no. 2, pp. 151-166.

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The L-transformation is quadratic in the projective 3-space and originally based on an irreducible spatial cubic. Here the case is addressed where the cubic splits into a conic and a straight line. Two cases are distinguished depending on whether the conic and the line are disjoint or not. An analytic representation of the L-transformation is given and the images of planes and lines are studied in detail. Keywords: Lambda-transformation, quadratic transformation. Classification: 51N15; 51N35. 
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     author = {E. Korczak},
     title = {A {Quadratic} {Transformation} {Based} on a {Straight} {Line} and a {Conic}},
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E. Korczak. A Quadratic Transformation Based on a Straight Line and a Conic. Journal for geometry and graphics, Tome 6 (2002) no. 2, pp. 151-166. http://geodesic.mathdoc.fr/item/JGG_2002_6_2_a4/