Random Gaussian cubic surface Seed: 419 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.233 x*z^2 -0.069 y*z^2 +0.334 z^2 +0.116 x^2*z +0.0654 x*y*z +0.32 x*z -0.452 y^2*z +0.301 y*z -0.236 z -0.14 x^3 -0.122 x^2*y +0.333 x^2 -0.34 x*y^2 -0.104 x*y +0.181 x -0.0993 y^3 +0.134 y^2 -0.163 y +0.00515 1
Affine cubic: f(x,y,z) = -0.233 x*z^2 -0.069 y*z^2 +0.334 z^2 +0.116 x^2*z +0.0654 x*y*z +0.32 x*z -0.452 y^2*z +0.301 y*z -0.236 z -0.14 x^3 -0.122 x^2*y +0.333 x^2 -0.34 x*y^2 -0.104 x*y +0.181 x -0.0993 y^3 +0.134 y^2 -0.163 y +0.00515 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].