Random Gaussian cubic surface Seed: 92 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.571 x*z^2 -0.236 y*z^2 -0.315 z^2 -0.315 x^2*z -0.0971 x*y*z +0.257 x*z -0.174 y^2*z -0.00878 y*z -0.0587 z -0.0487 x^3 -0.092 x^2*y +0.33 x^2 +0.15 x*y^2 -0.0478 x*y -0.33 x -0.197 y^3 -0.0989 y^2 -0.0904 y -0.013 1
Affine cubic: f(x,y,z) = -0.571 x*z^2 -0.236 y*z^2 -0.315 z^2 -0.315 x^2*z -0.0971 x*y*z +0.257 x*z -0.174 y^2*z -0.00878 y*z -0.0587 z -0.0487 x^3 -0.092 x^2*y +0.33 x^2 +0.15 x*y^2 -0.0478 x*y -0.33 x -0.197 y^3 -0.0989 y^2 -0.0904 y -0.013 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].