Random Gaussian cubic surface Seed: 329 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.218 x*z^2 -0.0497 y*z^2 -0.231 z^2 +0.433 x^2*z -0.349 x*y*z -0.216 x*z +0.0945 y^2*z -0.274 y*z -0.00343 z -0.276 x^3 +0.000983 x^2*y -0.0951 x^2 -0.355 x*y^2 +0.258 x*y -0.238 x +0.251 y^3 -0.0668 y^2 +0.149 y +0.182 1
Affine cubic: f(x,y,z) = 0.218 x*z^2 -0.0497 y*z^2 -0.231 z^2 +0.433 x^2*z -0.349 x*y*z -0.216 x*z +0.0945 y^2*z -0.274 y*z -0.00343 z -0.276 x^3 +0.000983 x^2*y -0.0951 x^2 -0.355 x*y^2 +0.258 x*y -0.238 x +0.251 y^3 -0.0668 y^2 +0.149 y +0.182 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].