Random Gaussian cubic surface Seed: 234 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.114 x*z^2 +0.143 y*z^2 +0.112 z^2 +0.132 x^2*z -0.00406 x*y*z +0.0293 x*z -0.322 y^2*z -0.181 y*z +0.197 z +0.104 x^3 -0.653 x^2*y +0.453 x^2 -0.0846 x*y^2 +0.104 x*y -0.236 x +0.109 y^3 +0.0344 y^2 -0.169 y +0.0534 1
Affine cubic: f(x,y,z) = 0.114 x*z^2 +0.143 y*z^2 +0.112 z^2 +0.132 x^2*z -0.00406 x*y*z +0.0293 x*z -0.322 y^2*z -0.181 y*z +0.197 z +0.104 x^3 -0.653 x^2*y +0.453 x^2 -0.0846 x*y^2 +0.104 x*y -0.236 x +0.109 y^3 +0.0344 y^2 -0.169 y +0.0534 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].