Random Gaussian cubic surface Seed: 22 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.263 x*z^2 -0.227 y*z^2 -0.245 z^2 -0.117 x^2*z +0.273 x*y*z -0.302 x*z +0.178 y^2*z +0.238 y*z -0.067 z -0.132 x^3 +0.0889 x^2*y +0.229 x^2 +0.406 x*y^2 +0.168 x*y +0.3 x -0.0848 y^3 -0.165 y^2 -0.324 y -0.217 1
Affine cubic: f(x,y,z) = -0.263 x*z^2 -0.227 y*z^2 -0.245 z^2 -0.117 x^2*z +0.273 x*y*z -0.302 x*z +0.178 y^2*z +0.238 y*z -0.067 z -0.132 x^3 +0.0889 x^2*y +0.229 x^2 +0.406 x*y^2 +0.168 x*y +0.3 x -0.0848 y^3 -0.165 y^2 -0.324 y -0.217 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 7 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].