Random Gaussian cubic surface Seed: 361 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.00709 x*z^2 +0.0981 y*z^2 -0.131 z^2 +0.418 x^2*z -0.465 x*y*z -0.263 x*z +0.222 y^2*z -0.0647 y*z +0.053 z -0.0712 x^3 +0.182 x^2*y +0.277 x^2 +0.309 x*y^2 +0.0868 x*y +0.00977 x -0.249 y^3 -0.0758 y^2 +0.255 y +0.324 1
Affine cubic: f(x,y,z) = 0.00709 x*z^2 +0.0981 y*z^2 -0.131 z^2 +0.418 x^2*z -0.465 x*y*z -0.263 x*z +0.222 y^2*z -0.0647 y*z +0.053 z -0.0712 x^3 +0.182 x^2*y +0.277 x^2 +0.309 x*y^2 +0.0868 x*y +0.00977 x -0.249 y^3 -0.0758 y^2 +0.255 y +0.324 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].