Random Gaussian cubic surface Seed: 411 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.144 x*z^2 -0.0883 y*z^2 +0.375 z^2 +0.00277 x^2*z +0.0809 x*y*z +0.198 x*z -0.0552 y^2*z -0.502 y*z +0.28 z -0.238 x^3 -0.145 x^2*y -0.0277 x^2 -0.199 x*y^2 -0.147 x*y +0.0524 x +0.137 y^3 +0.122 y^2 -0.0458 y +0.523 1
Affine cubic: f(x,y,z) = -0.144 x*z^2 -0.0883 y*z^2 +0.375 z^2 +0.00277 x^2*z +0.0809 x*y*z +0.198 x*z -0.0552 y^2*z -0.502 y*z +0.28 z -0.238 x^3 -0.145 x^2*y -0.0277 x^2 -0.199 x*y^2 -0.147 x*y +0.0524 x +0.137 y^3 +0.122 y^2 -0.0458 y +0.523 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].