Random Gaussian cubic surface Seed: 309 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.292 x*z^2 +0.205 y*z^2 -0.12 z^2 -0.318 x^2*z -0.458 x*y*z +0.00828 x*z -0.0248 y^2*z -0.149 y*z +0.191 z -0.321 x^3 -0.101 x^2*y +0.234 x^2 -0.0888 x*y^2 +0.119 x*y -0.412 x -0.0613 y^3 +0.098 y^2 +0.14 y +0.308 1
Affine cubic: f(x,y,z) = -0.292 x*z^2 +0.205 y*z^2 -0.12 z^2 -0.318 x^2*z -0.458 x*y*z +0.00828 x*z -0.0248 y^2*z -0.149 y*z +0.191 z -0.321 x^3 -0.101 x^2*y +0.234 x^2 -0.0888 x*y^2 +0.119 x*y -0.412 x -0.0613 y^3 +0.098 y^2 +0.14 y +0.308 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].