Random Gaussian cubic surface Seed: 475 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.086 x*z^2 -0.161 y*z^2 +0.378 z^2 +0.247 x^2*z +0.108 x*y*z +0.291 x*z -0.269 y^2*z +0.131 y*z -0.0281 z +0.0764 x^3 -0.0666 x^2*y +0.0982 x^2 -0.0789 x*y^2 -0.455 x*y +0.0318 x -0.509 y^3 -0.0192 y^2 -0.0246 y +0.286 1
Affine cubic: f(x,y,z) = 0.086 x*z^2 -0.161 y*z^2 +0.378 z^2 +0.247 x^2*z +0.108 x*y*z +0.291 x*z -0.269 y^2*z +0.131 y*z -0.0281 z +0.0764 x^3 -0.0666 x^2*y +0.0982 x^2 -0.0789 x*y^2 -0.455 x*y +0.0318 x -0.509 y^3 -0.0192 y^2 -0.0246 y +0.286 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].