Random Gaussian cubic surface Seed: 253 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0118 x*z^2 -0.0327 y*z^2 +0.218 z^2 +0.505 x^2*z -0.0608 x*y*z -0.3 x*z +0.145 y^2*z +0.209 y*z -0.261 z +0.337 x^3 +0.286 x^2*y +0.103 x^2 -0.317 x*y^2 +0.155 x*y +0.0484 x -0.134 y^3 -0.319 y^2 -0.124 y +0.0438 1
Affine cubic: f(x,y,z) = 0.0118 x*z^2 -0.0327 y*z^2 +0.218 z^2 +0.505 x^2*z -0.0608 x*y*z -0.3 x*z +0.145 y^2*z +0.209 y*z -0.261 z +0.337 x^3 +0.286 x^2*y +0.103 x^2 -0.317 x*y^2 +0.155 x*y +0.0484 x -0.134 y^3 -0.319 y^2 -0.124 y +0.0438 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 7 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].