Random Gaussian cubic surface Seed: 302 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.00492 x*z^2 -0.123 y*z^2 -0.45 z^2 -0.0371 x^2*z -0.0823 x*y*z +0.326 x*z +0.265 y^2*z +0.113 y*z +0.447 z +0.289 x^3 +0.089 x^2*y -0.392 x^2 -0.178 x*y^2 +0.016 x*y -0.229 x +0.192 y^3 -0.0582 y^2 +0.0191 y -0.123 1
Affine cubic: f(x,y,z) = -0.00492 x*z^2 -0.123 y*z^2 -0.45 z^2 -0.0371 x^2*z -0.0823 x*y*z +0.326 x*z +0.265 y^2*z +0.113 y*z +0.447 z +0.289 x^3 +0.089 x^2*y -0.392 x^2 -0.178 x*y^2 +0.016 x*y -0.229 x +0.192 y^3 -0.0582 y^2 +0.0191 y -0.123 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].