Random Gaussian cubic surface Seed: 382 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.099 x*z^2 -0.0708 y*z^2 +0.276 z^2 +0.248 x^2*z -0.0691 x*y*z +0.148 x*z -0.0369 y^2*z +0.215 y*z -0.00243 z +0.361 x^3 +0.271 x^2*y -0.29 x^2 +0.0317 x*y^2 -0.0641 x*y -0.217 x -0.0321 y^3 +0.643 y^2 +0.123 y +0.0621 1
Affine cubic: f(x,y,z) = 0.099 x*z^2 -0.0708 y*z^2 +0.276 z^2 +0.248 x^2*z -0.0691 x*y*z +0.148 x*z -0.0369 y^2*z +0.215 y*z -0.00243 z +0.361 x^3 +0.271 x^2*y -0.29 x^2 +0.0317 x*y^2 -0.0641 x*y -0.217 x -0.0321 y^3 +0.643 y^2 +0.123 y +0.0621 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].