Random Gaussian cubic surface Seed: 118 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.135 x*z^2 +0.122 y*z^2 +0.0296 z^2 -0.507 x^2*z +0.0926 x*y*z -0.0591 x*z -0.131 y^2*z +0.0795 y*z +0.208 z -0.00775 x^3 -0.358 x^2*y -0.139 x^2 +0.105 x*y^2 +0.157 x*y -0.238 x -0.32 y^3 -0.0128 y^2 +0.348 y +0.408 1
Affine cubic: f(x,y,z) = -0.135 x*z^2 +0.122 y*z^2 +0.0296 z^2 -0.507 x^2*z +0.0926 x*y*z -0.0591 x*z -0.131 y^2*z +0.0795 y*z +0.208 z -0.00775 x^3 -0.358 x^2*y -0.139 x^2 +0.105 x*y^2 +0.157 x*y -0.238 x -0.32 y^3 -0.0128 y^2 +0.348 y +0.408 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].