Random Gaussian cubic surface Seed: 143 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.235 x*z^2 +0.294 y*z^2 +0.0109 z^2 +0.104 x^2*z -0.335 x*y*z -0.0157 x*z -0.0285 y^2*z +0.337 y*z -0.222 z +0.00094 x^3 -0.412 x^2*y -0.0353 x^2 -0.164 x*y^2 -0.212 x*y -0.505 x +0.199 y^3 +0.0863 y^2 -0.155 y +0.0582 1
Affine cubic: f(x,y,z) = -0.235 x*z^2 +0.294 y*z^2 +0.0109 z^2 +0.104 x^2*z -0.335 x*y*z -0.0157 x*z -0.0285 y^2*z +0.337 y*z -0.222 z +0.00094 x^3 -0.412 x^2*y -0.0353 x^2 -0.164 x*y^2 -0.212 x*y -0.505 x +0.199 y^3 +0.0863 y^2 -0.155 y +0.0582 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].