Random Gaussian cubic surface Seed: 415 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0148 x*z^2 +0.332 y*z^2 -0.279 z^2 +0.204 x^2*z -0.159 x*y*z -0.345 x*z -0.351 y^2*z +0.0334 y*z -0.219 z -0.282 x^3 +0.208 x^2*y +0.00907 x^2 +0.0689 x*y^2 -0.132 x*y +0.0448 x -0.0569 y^3 +0.0736 y^2 +0.0738 y +0.54 1
Affine cubic: f(x,y,z) = 0.0148 x*z^2 +0.332 y*z^2 -0.279 z^2 +0.204 x^2*z -0.159 x*y*z -0.345 x*z -0.351 y^2*z +0.0334 y*z -0.219 z -0.282 x^3 +0.208 x^2*y +0.00907 x^2 +0.0689 x*y^2 -0.132 x*y +0.0448 x -0.0569 y^3 +0.0736 y^2 +0.0738 y +0.54 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].