Random Gaussian cubic surface Seed: 178 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0209 x*z^2 -0.124 y*z^2 +0.00717 z^2 -0.0152 x^2*z +0.0883 x*y*z -0.204 x*z +0.0883 y^2*z -0.478 y*z -0.292 z -0.291 x^3 -0.353 x^2*y +0.092 x^2 -0.292 x*y^2 +0.107 x*y +0.0729 x +0.193 y^3 +0.211 y^2 -0.357 y +0.289 1
Affine cubic: f(x,y,z) = -0.0209 x*z^2 -0.124 y*z^2 +0.00717 z^2 -0.0152 x^2*z +0.0883 x*y*z -0.204 x*z +0.0883 y^2*z -0.478 y*z -0.292 z -0.291 x^3 -0.353 x^2*y +0.092 x^2 -0.292 x*y^2 +0.107 x*y +0.0729 x +0.193 y^3 +0.211 y^2 -0.357 y +0.289 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].