Random Gaussian cubic surface Seed: 166 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.129 x*z^2 +0.201 y*z^2 +0.28 z^2 -0.0867 x^2*z +0.0629 x*y*z -0.143 x*z -0.111 y^2*z -0.0331 y*z +0.138 z +0.13 x^3 +0.328 x^2*y +0.192 x^2 -0.56 x*y^2 -0.112 x*y -0.197 x +0.0493 y^3 +0.0171 y^2 +0.372 y +0.364 1
Affine cubic: f(x,y,z) = -0.129 x*z^2 +0.201 y*z^2 +0.28 z^2 -0.0867 x^2*z +0.0629 x*y*z -0.143 x*z -0.111 y^2*z -0.0331 y*z +0.138 z +0.13 x^3 +0.328 x^2*y +0.192 x^2 -0.56 x*y^2 -0.112 x*y -0.197 x +0.0493 y^3 +0.0171 y^2 +0.372 y +0.364 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].