Random Gaussian cubic surface Seed: 339 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.192 x*z^2 -0.104 y*z^2 +0.0862 z^2 +0.163 x^2*z -0.396 x*y*z +0.141 x*z +0.354 y^2*z +0.0558 y*z +0.261 z +0.0902 x^3 -0.0735 x^2*y +0.143 x^2 -0.323 x*y^2 +0.128 x*y +0.128 x -0.433 y^3 +0.281 y^2 -0.00481 y +0.328 1
Affine cubic: f(x,y,z) = -0.192 x*z^2 -0.104 y*z^2 +0.0862 z^2 +0.163 x^2*z -0.396 x*y*z +0.141 x*z +0.354 y^2*z +0.0558 y*z +0.261 z +0.0902 x^3 -0.0735 x^2*y +0.143 x^2 -0.323 x*y^2 +0.128 x*y +0.128 x -0.433 y^3 +0.281 y^2 -0.00481 y +0.328 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].