Random Gaussian cubic surface Seed: 311 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.118 x*z^2 +0.2 y*z^2 +0.0171 z^2 +0.25 x^2*z -0.0588 x*y*z -0.184 x*z +0.377 y^2*z -0.216 y*z +0.164 z +0.262 x^3 -0.157 x^2*y +0.425 x^2 -0.197 x*y^2 -0.238 x*y -0.173 x +0.0852 y^3 -0.00984 y^2 -0.466 y +0.0768 1
Affine cubic: f(x,y,z) = 0.118 x*z^2 +0.2 y*z^2 +0.0171 z^2 +0.25 x^2*z -0.0588 x*y*z -0.184 x*z +0.377 y^2*z -0.216 y*z +0.164 z +0.262 x^3 -0.157 x^2*y +0.425 x^2 -0.197 x*y^2 -0.238 x*y -0.173 x +0.0852 y^3 -0.00984 y^2 -0.466 y +0.0768 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].