Random Gaussian cubic surface Seed: 80 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.235 x*z^2 -0.1 y*z^2 -0.141 z^2 -0.292 x^2*z -0.287 x*y*z +0.622 x*z +0.0324 y^2*z +0.0273 y*z +0.211 z +0.0709 x^3 -0.226 x^2*y -0.24 x^2 +0.104 x*y^2 -0.164 x*y +0.226 x -0.124 y^3 -0.224 y^2 -0.0624 y -0.201 1
Affine cubic: f(x,y,z) = 0.235 x*z^2 -0.1 y*z^2 -0.141 z^2 -0.292 x^2*z -0.287 x*y*z +0.622 x*z +0.0324 y^2*z +0.0273 y*z +0.211 z +0.0709 x^3 -0.226 x^2*y -0.24 x^2 +0.104 x*y^2 -0.164 x*y +0.226 x -0.124 y^3 -0.224 y^2 -0.0624 y -0.201 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].