Random Gaussian cubic surface Seed: 374 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.493 x*z^2 -0.0723 y*z^2 -0.0477 z^2 -0.135 x^2*z -0.179 x*y*z +0.255 x*z +0.372 y^2*z +0.268 y*z -0.288 z -0.146 x^3 -0.29 x^2*y +0.0372 x^2 -0.00275 x*y^2 +0.31 x*y +0.129 x -0.0452 y^3 -0.295 y^2 +0.0283 y -0.178 1
Affine cubic: f(x,y,z) = 0.493 x*z^2 -0.0723 y*z^2 -0.0477 z^2 -0.135 x^2*z -0.179 x*y*z +0.255 x*z +0.372 y^2*z +0.268 y*z -0.288 z -0.146 x^3 -0.29 x^2*y +0.0372 x^2 -0.00275 x*y^2 +0.31 x*y +0.129 x -0.0452 y^3 -0.295 y^2 +0.0283 y -0.178 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].