Random Gaussian cubic surface Seed: 232 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.218 x*z^2 +0.1 y*z^2 -0.161 z^2 -0.047 x^2*z -0.391 x*y*z +0.0563 x*z -0.212 y^2*z +0.451 y*z +0.0444 z -0.165 x^3 +0.0244 x^2*y +0.103 x^2 -0.212 x*y^2 -0.229 x*y +0.112 x +0.575 y^3 +0.00402 y^2 +0.0391 y +0.164 1
Affine cubic: f(x,y,z) = 0.218 x*z^2 +0.1 y*z^2 -0.161 z^2 -0.047 x^2*z -0.391 x*y*z +0.0563 x*z -0.212 y^2*z +0.451 y*z +0.0444 z -0.165 x^3 +0.0244 x^2*y +0.103 x^2 -0.212 x*y^2 -0.229 x*y +0.112 x +0.575 y^3 +0.00402 y^2 +0.0391 y +0.164 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].