Random Gaussian cubic surface Seed: 82 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.371 x*z^2 +0.22 y*z^2 +0.238 z^2 -0.208 x^2*z -0.13 x*y*z -0.163 x*z -0.366 y^2*z -0.0889 y*z +0.186 z +0.0409 x^3 -0.047 x^2*y -0.331 x^2 +0.395 x*y^2 -0.317 x*y +0.243 x -0.175 y^3 +0.0349 y^2 +0.0218 y -0.182 1
Affine cubic: f(x,y,z) = 0.371 x*z^2 +0.22 y*z^2 +0.238 z^2 -0.208 x^2*z -0.13 x*y*z -0.163 x*z -0.366 y^2*z -0.0889 y*z +0.186 z +0.0409 x^3 -0.047 x^2*y -0.331 x^2 +0.395 x*y^2 -0.317 x*y +0.243 x -0.175 y^3 +0.0349 y^2 +0.0218 y -0.182 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].