Random Gaussian cubic surface Seed: 493 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.249 x*z^2 +0.00972 y*z^2 +0.132 z^2 -0.0439 x^2*z -0.252 x*y*z -0.368 x*z -0.03 y^2*z -0.0623 y*z +0.000126 z -0.0766 x^3 +0.376 x^2*y -0.0881 x^2 -0.0472 x*y^2 -0.224 x*y +0.632 x +0.0827 y^3 +0.264 y^2 -0.0922 y -0.153 1
Affine cubic: f(x,y,z) = 0.249 x*z^2 +0.00972 y*z^2 +0.132 z^2 -0.0439 x^2*z -0.252 x*y*z -0.368 x*z -0.03 y^2*z -0.0623 y*z +0.000126 z -0.0766 x^3 +0.376 x^2*y -0.0881 x^2 -0.0472 x*y^2 -0.224 x*y +0.632 x +0.0827 y^3 +0.264 y^2 -0.0922 y -0.153 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].