Random Gaussian cubic surface Seed: 440 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.284 x*z^2 -0.134 y*z^2 +0.46 z^2 +0.168 x^2*z -0.0642 x*y*z -0.449 x*z +0.297 y^2*z -0.0635 y*z +0.15 z +0.207 x^3 -0.0242 x^2*y +0.0251 x^2 +0.134 x*y^2 +0.0534 x*y -0.215 x -0.0754 y^3 -0.225 y^2 +0.0338 y -0.416 1
Affine cubic: f(x,y,z) = -0.284 x*z^2 -0.134 y*z^2 +0.46 z^2 +0.168 x^2*z -0.0642 x*y*z -0.449 x*z +0.297 y^2*z -0.0635 y*z +0.15 z +0.207 x^3 -0.0242 x^2*y +0.0251 x^2 +0.134 x*y^2 +0.0534 x*y -0.215 x -0.0754 y^3 -0.225 y^2 +0.0338 y -0.416 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 7 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].