Random Gaussian cubic surface Seed: 169 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.247 x*z^2 -0.0458 y*z^2 +0.433 z^2 +0.287 x^2*z +0.0715 x*y*z +0.147 x*z -0.104 y^2*z -0.381 y*z +0.184 z -0.2 x^3 -0.106 x^2*y -0.131 x^2 -0.0487 x*y^2 -0.0555 x*y +0.0738 x +0.0507 y^3 -0.133 y^2 -0.532 y +0.261 1
Affine cubic: f(x,y,z) = 0.247 x*z^2 -0.0458 y*z^2 +0.433 z^2 +0.287 x^2*z +0.0715 x*y*z +0.147 x*z -0.104 y^2*z -0.381 y*z +0.184 z -0.2 x^3 -0.106 x^2*y -0.131 x^2 -0.0487 x*y^2 -0.0555 x*y +0.0738 x +0.0507 y^3 -0.133 y^2 -0.532 y +0.261 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].