Random Gaussian cubic surface Seed: 13 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.349 x*z^2 -0.588 y*z^2 +0.183 z^2 +0.0133 x^2*z +0.252 x*y*z +0.0736 x*z +0.349 y^2*z +0.00606 y*z -0.0986 z +0.111 x^3 +0.0825 x^2*y -0.0681 x^2 -0.0472 x*y^2 +0.137 x*y +0.135 x -0.0943 y^3 -0.0702 y^2 -0.345 y +0.321 1
Affine cubic: f(x,y,z) = 0.349 x*z^2 -0.588 y*z^2 +0.183 z^2 +0.0133 x^2*z +0.252 x*y*z +0.0736 x*z +0.349 y^2*z +0.00606 y*z -0.0986 z +0.111 x^3 +0.0825 x^2*y -0.0681 x^2 -0.0472 x*y^2 +0.137 x*y +0.135 x -0.0943 y^3 -0.0702 y^2 -0.345 y +0.321 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].