Random Gaussian cubic surface Seed: 432 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.155 x*z^2 -0.284 y*z^2 -0.296 z^2 -0.0141 x^2*z +0.0188 x*y*z -0.128 x*z -0.244 y^2*z +0.0522 y*z -0.107 z +0.396 x^3 -0.117 x^2*y -0.436 x^2 +0.466 x*y^2 -0.208 x*y -0.178 x +0.0784 y^3 +0.061 y^2 +0.171 y +0.159 1
Affine cubic: f(x,y,z) = 0.155 x*z^2 -0.284 y*z^2 -0.296 z^2 -0.0141 x^2*z +0.0188 x*y*z -0.128 x*z -0.244 y^2*z +0.0522 y*z -0.107 z +0.396 x^3 -0.117 x^2*y -0.436 x^2 +0.466 x*y^2 -0.208 x*y -0.178 x +0.0784 y^3 +0.061 y^2 +0.171 y +0.159 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].