Random Gaussian cubic surface Seed: 324 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.231 x*z^2 +0.421 y*z^2 +0.0855 z^2 -0.0977 x^2*z -0.225 x*y*z +0.338 x*z +0.0892 y^2*z +0.0587 y*z +0.496 z -0.242 x^3 +0.0138 x^2*y +0.105 x^2 +0.309 x*y^2 +0.0746 x*y -0.133 x -0.0778 y^3 +0.218 y^2 +0.186 y +0.232 1
Affine cubic: f(x,y,z) = -0.231 x*z^2 +0.421 y*z^2 +0.0855 z^2 -0.0977 x^2*z -0.225 x*y*z +0.338 x*z +0.0892 y^2*z +0.0587 y*z +0.496 z -0.242 x^3 +0.0138 x^2*y +0.105 x^2 +0.309 x*y^2 +0.0746 x*y -0.133 x -0.0778 y^3 +0.218 y^2 +0.186 y +0.232 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].