Random Gaussian cubic surface Seed: 3 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.369 x*z^2 -0.462 y*z^2 +0.0757 z^2 -0.103 x^2*z -0.0819 x*y*z -0.039 x*z -0.366 y^2*z -0.042 y*z -0.157 z +0.601 x^3 +0.0409 x^2*y -0.0638 x^2 -0.0509 x*y^2 -0.121 x*y -0.191 x -0.0707 y^3 +0.0872 y^2 -0.0432 y +0.173 1
Affine cubic: f(x,y,z) = 0.369 x*z^2 -0.462 y*z^2 +0.0757 z^2 -0.103 x^2*z -0.0819 x*y*z -0.039 x*z -0.366 y^2*z -0.042 y*z -0.157 z +0.601 x^3 +0.0409 x^2*y -0.0638 x^2 -0.0509 x*y^2 -0.121 x*y -0.191 x -0.0707 y^3 +0.0872 y^2 -0.0432 y +0.173 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 3 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].