Random Gaussian cubic surface Seed: 235 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.532 x*z^2 +0.209 y*z^2 +0.316 z^2 +0.0292 x^2*z -0.312 x*y*z -0.329 x*z -0.0555 y^2*z -0.0558 y*z -0.258 z +0.125 x^3 +0.239 x^2*y -0.287 x^2 -0.11 x*y^2 +0.0702 x*y +0.0874 x +0.123 y^3 -0.241 y^2 +0.131 y +0.154 1
Affine cubic: f(x,y,z) = 0.532 x*z^2 +0.209 y*z^2 +0.316 z^2 +0.0292 x^2*z -0.312 x*y*z -0.329 x*z -0.0555 y^2*z -0.0558 y*z -0.258 z +0.125 x^3 +0.239 x^2*y -0.287 x^2 -0.11 x*y^2 +0.0702 x*y +0.0874 x +0.123 y^3 -0.241 y^2 +0.131 y +0.154 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].