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 
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/
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     author = {E. Korczak},
     title = {A {Quadratic} {Transformation} {Based} on a {Straight} {Line} and a {Conic}},
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     pages = {151--166},
     year = {2002},
     volume = {6},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2002_6_2_a4/}
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Voir la notice de l'article provenant de la source Heldermann Verlag

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.