Random Gaussian cubic surface Seed: 478 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.267 x*z^2 +0.304 y*z^2 +0.00496 z^2 +0.297 x^2*z -0.2 x*y*z -0.279 x*z -0.139 y^2*z +0.261 y*z +0.121 z +0.0498 x^3 +0.43 x^2*y +0.00522 x^2 -0.0611 x*y^2 -0.0625 x*y -0.00418 x +0.35 y^3 -0.388 y^2 +0.246 y +0.0216 1
Affine cubic: f(x,y,z) = 0.267 x*z^2 +0.304 y*z^2 +0.00496 z^2 +0.297 x^2*z -0.2 x*y*z -0.279 x*z -0.139 y^2*z +0.261 y*z +0.121 z +0.0498 x^3 +0.43 x^2*y +0.00522 x^2 -0.0611 x*y^2 -0.0625 x*y -0.00418 x +0.35 y^3 -0.388 y^2 +0.246 y +0.0216 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].