Random Gaussian cubic surface Seed: 333 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.202 x*z^2 +0.459 y*z^2 -0.152 z^2 +0.229 x^2*z +0.109 x*y*z +0.0518 x*z -0.123 y^2*z +0.226 y*z -0.248 z -0.426 x^3 -0.254 x^2*y +0.151 x^2 -0.162 x*y^2 +0.268 x*y +0.09 x +0.164 y^3 +0.328 y^2 -0.00237 y +0.145 1
Affine cubic: f(x,y,z) = -0.202 x*z^2 +0.459 y*z^2 -0.152 z^2 +0.229 x^2*z +0.109 x*y*z +0.0518 x*z -0.123 y^2*z +0.226 y*z -0.248 z -0.426 x^3 -0.254 x^2*y +0.151 x^2 -0.162 x*y^2 +0.268 x*y +0.09 x +0.164 y^3 +0.328 y^2 -0.00237 y +0.145 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].