Random Gaussian cubic surface Seed: 345 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0318 x*z^2 -0.0946 y*z^2 +0.161 z^2 -0.232 x^2*z +0.0231 x*y*z -0.314 x*z +0.0475 y^2*z -0.417 y*z +0.0306 z +0.101 x^3 -0.543 x^2*y +0.0405 x^2 -0.0704 x*y^2 +0.114 x*y -0.0163 x -0.00496 y^3 +0.238 y^2 +0.35 y +0.36 1
Affine cubic: f(x,y,z) = 0.0318 x*z^2 -0.0946 y*z^2 +0.161 z^2 -0.232 x^2*z +0.0231 x*y*z -0.314 x*z +0.0475 y^2*z -0.417 y*z +0.0306 z +0.101 x^3 -0.543 x^2*y +0.0405 x^2 -0.0704 x*y^2 +0.114 x*y -0.0163 x -0.00496 y^3 +0.238 y^2 +0.35 y +0.36 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].