Random Gaussian cubic surface Seed: 355 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.199 x*z^2 -0.141 y*z^2 +0.277 z^2 +0.134 x^2*z +0.206 x*y*z +0.192 x*z -0.216 y^2*z +0.0395 y*z -0.518 z -0.0444 x^3 -0.107 x^2*y +0.231 x^2 +0.145 x*y^2 -0.326 x*y +0.287 x +0.0523 y^3 +0.0562 y^2 -0.0783 y +0.401 1
Affine cubic: f(x,y,z) = -0.199 x*z^2 -0.141 y*z^2 +0.277 z^2 +0.134 x^2*z +0.206 x*y*z +0.192 x*z -0.216 y^2*z +0.0395 y*z -0.518 z -0.0444 x^3 -0.107 x^2*y +0.231 x^2 +0.145 x*y^2 -0.326 x*y +0.287 x +0.0523 y^3 +0.0562 y^2 -0.0783 y +0.401 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].