Random Gaussian cubic surface Seed: 369 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.038 x*z^2 +0.00502 y*z^2 +0.2 z^2 -0.11 x^2*z +0.0377 x*y*z +0.042 x*z -0.118 y^2*z +0.0389 y*z +0.0053 z +0.315 x^3 +0.138 x^2*y -0.516 x^2 -0.0798 x*y^2 +0.021 x*y -0.473 x -0.426 y^3 +0.0305 y^2 -0.273 y +0.235 1
Affine cubic: f(x,y,z) = 0.038 x*z^2 +0.00502 y*z^2 +0.2 z^2 -0.11 x^2*z +0.0377 x*y*z +0.042 x*z -0.118 y^2*z +0.0389 y*z +0.0053 z +0.315 x^3 +0.138 x^2*y -0.516 x^2 -0.0798 x*y^2 +0.021 x*y -0.473 x -0.426 y^3 +0.0305 y^2 -0.273 y +0.235 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].