Random Gaussian cubic surface Seed: 160 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.31 x*z^2 +0.0891 y*z^2 -0.214 z^2 +0.0406 x^2*z -0.0331 x*y*z -0.516 x*z +0.362 y^2*z -0.0357 y*z +0.178 z +0.0833 x^3 +0.14 x^2*y -0.031 x^2 +0.0315 x*y^2 +0.0233 x*y +0.13 x +0.235 y^3 +0.377 y^2 +0.358 y -0.215 1
Affine cubic: f(x,y,z) = -0.31 x*z^2 +0.0891 y*z^2 -0.214 z^2 +0.0406 x^2*z -0.0331 x*y*z -0.516 x*z +0.362 y^2*z -0.0357 y*z +0.178 z +0.0833 x^3 +0.14 x^2*y -0.031 x^2 +0.0315 x*y^2 +0.0233 x*y +0.13 x +0.235 y^3 +0.377 y^2 +0.358 y -0.215 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].