Random Gaussian cubic surface Seed: 27 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.294 x*z^2 +0.182 y*z^2 +0.226 z^2 -0.254 x^2*z +0.203 x*y*z -0.0395 x*z -0.0445 y^2*z +0.263 y*z -0.102 z -0.3 x^3 -0.11 x^2*y -0.281 x^2 -0.432 x*y^2 -0.0342 x*y +0.0934 x -0.507 y^3 +0.0034 y^2 +0.0599 y +0.0406 1
Affine cubic: f(x,y,z) = 0.294 x*z^2 +0.182 y*z^2 +0.226 z^2 -0.254 x^2*z +0.203 x*y*z -0.0395 x*z -0.0445 y^2*z +0.263 y*z -0.102 z -0.3 x^3 -0.11 x^2*y -0.281 x^2 -0.432 x*y^2 -0.0342 x*y +0.0934 x -0.507 y^3 +0.0034 y^2 +0.0599 y +0.0406 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].