Random Gaussian cubic surface Seed: 241 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.367 x*z^2 +0.361 y*z^2 +0.284 z^2 +0.134 x^2*z -0.0907 x*y*z -0.0621 x*z +0.264 y^2*z -0.48 y*z -0.186 z -0.00338 x^3 -0.0098 x^2*y +0.325 x^2 -0.159 x*y^2 +0.0287 x*y -0.11 x -0.112 y^3 -0.279 y^2 +0.226 y +0.0526 1
Affine cubic: f(x,y,z) = -0.367 x*z^2 +0.361 y*z^2 +0.284 z^2 +0.134 x^2*z -0.0907 x*y*z -0.0621 x*z +0.264 y^2*z -0.48 y*z -0.186 z -0.00338 x^3 -0.0098 x^2*y +0.325 x^2 -0.159 x*y^2 +0.0287 x*y -0.11 x -0.112 y^3 -0.279 y^2 +0.226 y +0.0526 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 15 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].