Random Gaussian cubic surface Seed: 343 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0953 x*z^2 +0.195 y*z^2 -0.0478 z^2 +0.399 x^2*z -0.202 x*y*z +0.0551 x*z -0.0228 y^2*z -0.0704 y*z +0.0521 z -0.269 x^3 +0.442 x^2*y +0.0575 x^2 +0.232 x*y^2 +0.502 x*y +0.302 x +0.124 y^3 -0.0392 y^2 -0.213 y -0.0954 1
Affine cubic: f(x,y,z) = 0.0953 x*z^2 +0.195 y*z^2 -0.0478 z^2 +0.399 x^2*z -0.202 x*y*z +0.0551 x*z -0.0228 y^2*z -0.0704 y*z +0.0521 z -0.269 x^3 +0.442 x^2*y +0.0575 x^2 +0.232 x*y^2 +0.502 x*y +0.302 x +0.124 y^3 -0.0392 y^2 -0.213 y -0.0954 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].