Random Gaussian cubic surface Seed: 356 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0802 x*z^2 +0.0776 y*z^2 -0.00754 z^2 +0.0921 x^2*z -0.169 x*y*z -0.0927 x*z -0.169 y^2*z -0.487 y*z -0.00957 z -0.0192 x^3 +0.192 x^2*y +0.448 x^2 +0.0445 x*y^2 -0.235 x*y -0.162 x +0.0666 y^3 +0.513 y^2 +0.00897 y +0.295 1
Affine cubic: f(x,y,z) = -0.0802 x*z^2 +0.0776 y*z^2 -0.00754 z^2 +0.0921 x^2*z -0.169 x*y*z -0.0927 x*z -0.169 y^2*z -0.487 y*z -0.00957 z -0.0192 x^3 +0.192 x^2*y +0.448 x^2 +0.0445 x*y^2 -0.235 x*y -0.162 x +0.0666 y^3 +0.513 y^2 +0.00897 y +0.295 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].