Random Gaussian cubic surface Seed: 33 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.104 x*z^2 -0.146 y*z^2 +0.153 z^2 +0.011 x^2*z -0.409 x*y*z +0.261 x*z -0.0255 y^2*z +0.161 y*z +0.478 z +0.0698 x^3 -0.279 x^2*y -0.177 x^2 +0.264 x*y^2 -0.379 x*y +0.0686 x +0.0976 y^3 -0.299 y^2 +0.044 y +0.145 1
Affine cubic: f(x,y,z) = 0.104 x*z^2 -0.146 y*z^2 +0.153 z^2 +0.011 x^2*z -0.409 x*y*z +0.261 x*z -0.0255 y^2*z +0.161 y*z +0.478 z +0.0698 x^3 -0.279 x^2*y -0.177 x^2 +0.264 x*y^2 -0.379 x*y +0.0686 x +0.0976 y^3 -0.299 y^2 +0.044 y +0.145 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].