Random Gaussian cubic surface Seed: 473 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.12 x*z^2 +0.181 y*z^2 +0.267 z^2 +0.0367 x^2*z -0.0333 x*y*z -0.0935 x*z +0.0574 y^2*z -0.161 y*z +0.076 z +0.0275 x^3 -0.383 x^2*y +0.00836 x^2 +0.718 x*y^2 -0.0454 x*y +0.0685 x -0.144 y^3 -0.307 y^2 +0.125 y -0.186 1
Affine cubic: f(x,y,z) = -0.12 x*z^2 +0.181 y*z^2 +0.267 z^2 +0.0367 x^2*z -0.0333 x*y*z -0.0935 x*z +0.0574 y^2*z -0.161 y*z +0.076 z +0.0275 x^3 -0.383 x^2*y +0.00836 x^2 +0.718 x*y^2 -0.0454 x*y +0.0685 x -0.144 y^3 -0.307 y^2 +0.125 y -0.186 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].