Random Gaussian cubic surface Seed: 375 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.24 x*z^2 +0.179 y*z^2 -0.00177 z^2 -0.422 x^2*z +0.0812 x*y*z -0.0622 x*z +0.333 y^2*z +0.445 y*z -0.111 z +0.2 x^3 +0.358 x^2*y -0.0395 x^2 +0.0873 x*y^2 -0.0786 x*y +0.0455 x -0.0526 y^3 +0.107 y^2 +0.379 y -0.239 1
Affine cubic: f(x,y,z) = -0.24 x*z^2 +0.179 y*z^2 -0.00177 z^2 -0.422 x^2*z +0.0812 x*y*z -0.0622 x*z +0.333 y^2*z +0.445 y*z -0.111 z +0.2 x^3 +0.358 x^2*y -0.0395 x^2 +0.0873 x*y^2 -0.0786 x*y +0.0455 x -0.0526 y^3 +0.107 y^2 +0.379 y -0.239 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].