Random Gaussian cubic surface Seed: 266 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.39 x*z^2 -0.264 y*z^2 -0.0959 z^2 -0.0322 x^2*z -0.171 x*y*z -0.198 x*z -0.203 y^2*z -0.451 y*z +0.324 z +0.315 x^3 +0.153 x^2*y +0.171 x^2 -0.163 x*y^2 -0.0375 x*y +0.226 x +0.325 y^3 +0.0437 y^2 +0.0468 y -0.0971 1
Affine cubic: f(x,y,z) = 0.39 x*z^2 -0.264 y*z^2 -0.0959 z^2 -0.0322 x^2*z -0.171 x*y*z -0.198 x*z -0.203 y^2*z -0.451 y*z +0.324 z +0.315 x^3 +0.153 x^2*y +0.171 x^2 -0.163 x*y^2 -0.0375 x*y +0.226 x +0.325 y^3 +0.0437 y^2 +0.0468 y -0.0971 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].