Random Gaussian cubic surface Seed: 274 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.149 x*z^2 -0.187 y*z^2 -0.256 z^2 -0.117 x^2*z +0.0916 x*y*z -0.0506 x*z -0.144 y^2*z -0.377 y*z +0.0621 z +0.554 x^3 +0.128 x^2*y +0.0614 x^2 -0.224 x*y^2 -0.0721 x*y -0.412 x -0.0222 y^3 -0.0968 y^2 +0.0439 y -0.349 1
Affine cubic: f(x,y,z) = -0.149 x*z^2 -0.187 y*z^2 -0.256 z^2 -0.117 x^2*z +0.0916 x*y*z -0.0506 x*z -0.144 y^2*z -0.377 y*z +0.0621 z +0.554 x^3 +0.128 x^2*y +0.0614 x^2 -0.224 x*y^2 -0.0721 x*y -0.412 x -0.0222 y^3 -0.0968 y^2 +0.0439 y -0.349 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].