Random Gaussian cubic surface Seed: 255 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.162 x*z^2 -0.199 y*z^2 +0.0619 z^2 -0.242 x^2*z +0.169 x*y*z +0.103 x*z -0.0385 y^2*z -0.293 y*z +0.258 z -0.466 x^3 +0.496 x^2*y +0.0789 x^2 +0.137 x*y^2 +0.307 x*y -0.106 x +0.181 y^3 +0.0316 y^2 +0.163 y -0.158 1
Affine cubic: f(x,y,z) = 0.162 x*z^2 -0.199 y*z^2 +0.0619 z^2 -0.242 x^2*z +0.169 x*y*z +0.103 x*z -0.0385 y^2*z -0.293 y*z +0.258 z -0.466 x^3 +0.496 x^2*y +0.0789 x^2 +0.137 x*y^2 +0.307 x*y -0.106 x +0.181 y^3 +0.0316 y^2 +0.163 y -0.158 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 15 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].