Random Gaussian cubic surface Seed: 427 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0729 x*z^2 -0.484 y*z^2 +0.109 z^2 +0.0944 x^2*z -0.378 x*y*z -0.146 x*z +0.181 y^2*z +0.0627 y*z +0.0518 z -0.0717 x^3 -0.125 x^2*y -0.309 x^2 +0.0967 x*y^2 -0.552 x*y +0.28 x +0.0717 y^3 +0.0948 y^2 +0.119 y -0.00611 1
Affine cubic: f(x,y,z) = 0.0729 x*z^2 -0.484 y*z^2 +0.109 z^2 +0.0944 x^2*z -0.378 x*y*z -0.146 x*z +0.181 y^2*z +0.0627 y*z +0.0518 z -0.0717 x^3 -0.125 x^2*y -0.309 x^2 +0.0967 x*y^2 -0.552 x*y +0.28 x +0.0717 y^3 +0.0948 y^2 +0.119 y -0.00611 1
Shadow: the quartic B(x,y)^2 - 4 A(x,y) C(x,y) = 0 is drawn on the z=-4 xy-plane in the same 3D scene. The translucent ruled curtain rises upward from the shadow to the ramification curve where the lifted point has z >= -2 and lies above the displayed projection plane. The 7 real projected lines on the xy-plane are bitangents found from the projective lines on the cubic surface. Same-color transparent line projection cones are included but hidden by default; use the page toggle to show them.
Viewing box: axis ranges are [-4, 4].