Random Gaussian cubic surface Seed: 320 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.363 x*z^2 +0.232 y*z^2 +0.389 z^2 -0.0354 x^2*z +0.26 x*y*z -0.0853 x*z -0.15 y^2*z -0.046 y*z -0.172 z +0.07 x^3 +0.0208 x^2*y +0.118 x^2 +0.0432 x*y^2 +0.598 x*y -0.00943 x -0.202 y^3 +0.0665 y^2 -0.227 y +0.238 1
Affine cubic: f(x,y,z) = 0.363 x*z^2 +0.232 y*z^2 +0.389 z^2 -0.0354 x^2*z +0.26 x*y*z -0.0853 x*z -0.15 y^2*z -0.046 y*z -0.172 z +0.07 x^3 +0.0208 x^2*y +0.118 x^2 +0.0432 x*y^2 +0.598 x*y -0.00943 x -0.202 y^3 +0.0665 y^2 -0.227 y +0.238 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].