Random Gaussian cubic surface Seed: 167 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.341 x*z^2 -0.0977 y*z^2 +0.218 z^2 +0.259 x^2*z -0.188 x*y*z +0.0105 x*z +0.348 y^2*z +0.251 y*z -0.162 z -0.139 x^3 -0.274 x^2*y +0.02 x^2 -0.158 x*y^2 +0.252 x*y +0.103 x -0.0171 y^3 -0.493 y^2 +0.0159 y -0.275 1
Affine cubic: f(x,y,z) = 0.341 x*z^2 -0.0977 y*z^2 +0.218 z^2 +0.259 x^2*z -0.188 x*y*z +0.0105 x*z +0.348 y^2*z +0.251 y*z -0.162 z -0.139 x^3 -0.274 x^2*y +0.02 x^2 -0.158 x*y^2 +0.252 x*y +0.103 x -0.0171 y^3 -0.493 y^2 +0.0159 y -0.275 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].