Random Gaussian cubic surface Seed: 197 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.097 x*z^2 +0.0959 y*z^2 +0.168 z^2 -0.313 x^2*z +0.178 x*y*z -0.018 x*z -0.472 y^2*z +0.0762 y*z -0.0293 z +0.00754 x^3 -0.457 x^2*y +0.103 x^2 +0.078 x*y^2 +0.32 x*y +0.0823 x -0.141 y^3 +0.157 y^2 -0.00629 y +0.463 1
Affine cubic: f(x,y,z) = 0.097 x*z^2 +0.0959 y*z^2 +0.168 z^2 -0.313 x^2*z +0.178 x*y*z -0.018 x*z -0.472 y^2*z +0.0762 y*z -0.0293 z +0.00754 x^3 -0.457 x^2*y +0.103 x^2 +0.078 x*y^2 +0.32 x*y +0.0823 x -0.141 y^3 +0.157 y^2 -0.00629 y +0.463 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].