Random Gaussian cubic surface Seed: 448 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.125 x*z^2 -0.142 y*z^2 -0.217 z^2 -0.0813 x^2*z -0.212 x*y*z +0.0817 x*z -0.112 y^2*z -0.493 y*z -0.00884 z +0.161 x^3 +0.135 x^2*y +0.0996 x^2 -0.0186 x*y^2 -0.252 x*y -0.272 x +0.216 y^3 -0.0801 y^2 +0.529 y -0.28 1
Affine cubic: f(x,y,z) = 0.125 x*z^2 -0.142 y*z^2 -0.217 z^2 -0.0813 x^2*z -0.212 x*y*z +0.0817 x*z -0.112 y^2*z -0.493 y*z -0.00884 z +0.161 x^3 +0.135 x^2*y +0.0996 x^2 -0.0186 x*y^2 -0.252 x*y -0.272 x +0.216 y^3 -0.0801 y^2 +0.529 y -0.28 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].