Random Gaussian cubic surface Seed: 113 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.272 x*z^2 +0.0899 y*z^2 -0.0101 z^2 -0.381 x^2*z +0.168 x*y*z +0.418 x*z +0.423 y^2*z +0.0851 y*z -0.104 z +0.158 x^3 -0.343 x^2*y -0.0823 x^2 +0.109 x*y^2 +0.0798 x*y +0.067 x -0.254 y^3 -0.327 y^2 +0.0498 y +0.163 1
Affine cubic: f(x,y,z) = 0.272 x*z^2 +0.0899 y*z^2 -0.0101 z^2 -0.381 x^2*z +0.168 x*y*z +0.418 x*z +0.423 y^2*z +0.0851 y*z -0.104 z +0.158 x^3 -0.343 x^2*y -0.0823 x^2 +0.109 x*y^2 +0.0798 x*y +0.067 x -0.254 y^3 -0.327 y^2 +0.0498 y +0.163 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].