Random Gaussian cubic surface Seed: 136 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.00904 x*z^2 -0.366 y*z^2 +0.324 z^2 +0.363 x^2*z +0.194 x*y*z -0.0314 x*z -0.301 y^2*z +0.381 y*z +0.0965 z +0.0955 x^3 +0.0779 x^2*y +0.0842 x^2 -0.0339 x*y^2 +0.277 x*y -0.331 x +0.0017 y^3 -0.348 y^2 -0.0835 y +0.0887 1
Affine cubic: f(x,y,z) = 0.00904 x*z^2 -0.366 y*z^2 +0.324 z^2 +0.363 x^2*z +0.194 x*y*z -0.0314 x*z -0.301 y^2*z +0.381 y*z +0.0965 z +0.0955 x^3 +0.0779 x^2*y +0.0842 x^2 -0.0339 x*y^2 +0.277 x*y -0.331 x +0.0017 y^3 -0.348 y^2 -0.0835 y +0.0887 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 7 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].