Random Gaussian cubic surface Seed: 408 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.109 x*z^2 -0.436 y*z^2 -0.421 z^2 +0.0272 x^2*z +0.233 x*y*z -0.141 x*z -0.168 y^2*z +0.058 y*z -0.224 z +0.132 x^3 +0.248 x^2*y -0.119 x^2 +0.118 x*y^2 -0.212 x*y +0.216 x +0.166 y^3 +0.124 y^2 +0.338 y +0.329 1
Affine cubic: f(x,y,z) = -0.109 x*z^2 -0.436 y*z^2 -0.421 z^2 +0.0272 x^2*z +0.233 x*y*z -0.141 x*z -0.168 y^2*z +0.058 y*z -0.224 z +0.132 x^3 +0.248 x^2*y -0.119 x^2 +0.118 x*y^2 -0.212 x*y +0.216 x +0.166 y^3 +0.124 y^2 +0.338 y +0.329 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].