Random Gaussian cubic surface Seed: 450 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.542 x*z^2 +0.137 y*z^2 -0.0391 z^2 -0.00538 x^2*z +0.296 x*y*z +0.141 x*z +0.0135 y^2*z -0.101 y*z +0.038 z -0.0135 x^3 -0.122 x^2*y +0.419 x^2 +0.197 x*y^2 -0.249 x*y +0.499 x -0.141 y^3 -0.0318 y^2 +0.0613 y +0.0353 1
Affine cubic: f(x,y,z) = -0.542 x*z^2 +0.137 y*z^2 -0.0391 z^2 -0.00538 x^2*z +0.296 x*y*z +0.141 x*z +0.0135 y^2*z -0.101 y*z +0.038 z -0.0135 x^3 -0.122 x^2*y +0.419 x^2 +0.197 x*y^2 -0.249 x*y +0.499 x -0.141 y^3 -0.0318 y^2 +0.0613 y +0.0353 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 15 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].