Random Gaussian cubic surface Seed: 24 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.357 x*z^2 +0.0907 y*z^2 -0.308 z^2 -0.0495 x^2*z -0.0898 x*y*z -0.0602 x*z +0.158 y^2*z -0.338 y*z +0.256 z -0.298 x^3 -0.0498 x^2*y +0.235 x^2 +0.175 x*y^2 -0.183 x*y +0.468 x +0.0967 y^3 -0.252 y^2 +0.0112 y -0.22 1
Affine cubic: f(x,y,z) = 0.357 x*z^2 +0.0907 y*z^2 -0.308 z^2 -0.0495 x^2*z -0.0898 x*y*z -0.0602 x*z +0.158 y^2*z -0.338 y*z +0.256 z -0.298 x^3 -0.0498 x^2*y +0.235 x^2 +0.175 x*y^2 -0.183 x*y +0.468 x +0.0967 y^3 -0.252 y^2 +0.0112 y -0.22 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].