Random Gaussian cubic surface Seed: 18 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0876 x*z^2 -0.229 y*z^2 +0.137 z^2 -0.224 x^2*z +0.408 x*y*z +0.187 x*z -0.0728 y^2*z +0.116 y*z +0.327 z +0.574 x^3 -0.187 x^2*y +0.216 x^2 +0.105 x*y^2 -0.0566 x*y +0.221 x +0.103 y^3 +0.218 y^2 -0.107 y -0.000505 1
Affine cubic: f(x,y,z) = -0.0876 x*z^2 -0.229 y*z^2 +0.137 z^2 -0.224 x^2*z +0.408 x*y*z +0.187 x*z -0.0728 y^2*z +0.116 y*z +0.327 z +0.574 x^3 -0.187 x^2*y +0.216 x^2 +0.105 x*y^2 -0.0566 x*y +0.221 x +0.103 y^3 +0.218 y^2 -0.107 y -0.000505 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].