Random Gaussian cubic surface Seed: 321 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.204 x*z^2 +0.128 y*z^2 -0.444 z^2 -0.453 x^2*z -0.13 x*y*z -0.0403 x*z +0.137 y^2*z -0.266 y*z +0.508 z -0.265 x^3 +0.202 x^2*y -0.0207 x^2 -0.0617 x*y^2 +0.0937 x*y +0.0334 x +0.109 y^3 +0.103 y^2 -0.155 y -0.0493 1
Affine cubic: f(x,y,z) = -0.204 x*z^2 +0.128 y*z^2 -0.444 z^2 -0.453 x^2*z -0.13 x*y*z -0.0403 x*z +0.137 y^2*z -0.266 y*z +0.508 z -0.265 x^3 +0.202 x^2*y -0.0207 x^2 -0.0617 x*y^2 +0.0937 x*y +0.0334 x +0.109 y^3 +0.103 y^2 -0.155 y -0.0493 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].