Random Gaussian cubic surface Seed: 446 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.311 x*z^2 -0.219 y*z^2 +0.247 z^2 -0.191 x^2*z +0.345 x*y*z -0.241 x*z -0.345 y^2*z +0.111 y*z -0.0558 z -0.255 x^3 -0.0352 x^2*y +0.131 x^2 -0.268 x*y^2 -0.229 x*y -0.191 x +0.342 y^3 -0.111 y^2 -0.223 y +0.146 1
Affine cubic: f(x,y,z) = 0.311 x*z^2 -0.219 y*z^2 +0.247 z^2 -0.191 x^2*z +0.345 x*y*z -0.241 x*z -0.345 y^2*z +0.111 y*z -0.0558 z -0.255 x^3 -0.0352 x^2*y +0.131 x^2 -0.268 x*y^2 -0.229 x*y -0.191 x +0.342 y^3 -0.111 y^2 -0.223 y +0.146 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].