Random Gaussian cubic surface Seed: 75 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.288 x*z^2 +0.103 y*z^2 +0.105 z^2 +0.113 x^2*z +0.132 x*y*z +0.00641 x*z +0.116 y^2*z +0.276 y*z +0.48 z -0.0393 x^3 -0.211 x^2*y -0.366 x^2 +0.0697 x*y^2 -0.0423 x*y +0.415 x -0.335 y^3 -0.134 y^2 -0.232 y +0.0497 1
Affine cubic: f(x,y,z) = -0.288 x*z^2 +0.103 y*z^2 +0.105 z^2 +0.113 x^2*z +0.132 x*y*z +0.00641 x*z +0.116 y^2*z +0.276 y*z +0.48 z -0.0393 x^3 -0.211 x^2*y -0.366 x^2 +0.0697 x*y^2 -0.0423 x*y +0.415 x -0.335 y^3 -0.134 y^2 -0.232 y +0.0497 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].