Random Gaussian cubic surface Seed: 421 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.285 x*z^2 +0.337 y*z^2 -0.0963 z^2 +0.227 x^2*z -0.133 x*y*z +0.212 x*z -0.0316 y^2*z +0.155 y*z -0.587 z +0.0112 x^3 -0.173 x^2*y +0.414 x^2 -0.261 x*y^2 +0.107 x*y -0.0929 x +0.00912 y^3 +0.0564 y^2 +0.14 y -0.00029 1
Affine cubic: f(x,y,z) = 0.285 x*z^2 +0.337 y*z^2 -0.0963 z^2 +0.227 x^2*z -0.133 x*y*z +0.212 x*z -0.0316 y^2*z +0.155 y*z -0.587 z +0.0112 x^3 -0.173 x^2*y +0.414 x^2 -0.261 x*y^2 +0.107 x*y -0.0929 x +0.00912 y^3 +0.0564 y^2 +0.14 y -0.00029 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].