Random Gaussian cubic surface Seed: 250 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.222 x*z^2 -0.123 y*z^2 -0.211 z^2 -0.513 x^2*z +0.0691 x*y*z +0.23 x*z +0.134 y^2*z -0.161 y*z +0.163 z -0.338 x^3 -0.0665 x^2*y +0.0312 x^2 -0.0452 x*y^2 -0.142 x*y -0.189 x -0.0891 y^3 -0.132 y^2 -0.408 y +0.361 1
Affine cubic: f(x,y,z) = -0.222 x*z^2 -0.123 y*z^2 -0.211 z^2 -0.513 x^2*z +0.0691 x*y*z +0.23 x*z +0.134 y^2*z -0.161 y*z +0.163 z -0.338 x^3 -0.0665 x^2*y +0.0312 x^2 -0.0452 x*y^2 -0.142 x*y -0.189 x -0.0891 y^3 -0.132 y^2 -0.408 y +0.361 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].