Random Gaussian cubic surface Seed: 463 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.129 x*z^2 -0.0724 y*z^2 -0.123 z^2 -0.426 x^2*z +0.166 x*y*z -0.0328 x*z -0.33 y^2*z +0.0518 y*z +0.133 z -0.0761 x^3 +0.478 x^2*y -0.0154 x^2 -0.0375 x*y^2 +0.216 x*y -0.0473 x -0.167 y^3 -0.521 y^2 -0.0877 y -0.178 1
Affine cubic: f(x,y,z) = -0.129 x*z^2 -0.0724 y*z^2 -0.123 z^2 -0.426 x^2*z +0.166 x*y*z -0.0328 x*z -0.33 y^2*z +0.0518 y*z +0.133 z -0.0761 x^3 +0.478 x^2*y -0.0154 x^2 -0.0375 x*y^2 +0.216 x*y -0.0473 x -0.167 y^3 -0.521 y^2 -0.0877 y -0.178 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].