Random Gaussian cubic surface Seed: 125 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.478 x*z^2 -0.516 y*z^2 -0.0375 z^2 -0.0793 x^2*z -0.161 x*y*z -0.105 x*z -0.0955 y^2*z -0.262 y*z -0.186 z -0.204 x^3 -0.376 x^2*y -0.288 x^2 -0.254 x*y^2 +0.0613 x*y -0.0537 x +0.0791 y^3 -0.0332 y^2 +0.00781 y +0.0578 1
Affine cubic: f(x,y,z) = -0.478 x*z^2 -0.516 y*z^2 -0.0375 z^2 -0.0793 x^2*z -0.161 x*y*z -0.105 x*z -0.0955 y^2*z -0.262 y*z -0.186 z -0.204 x^3 -0.376 x^2*y -0.288 x^2 -0.254 x*y^2 +0.0613 x*y -0.0537 x +0.0791 y^3 -0.0332 y^2 +0.00781 y +0.0578 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].