Random Gaussian cubic surface Seed: 354 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.42 x*z^2 -0.121 y*z^2 +0.22 z^2 -0.17 x^2*z -0.325 x*y*z -0.0938 x*z +0.126 y^2*z -0.104 y*z -0.0762 z -0.642 x^3 +0.125 x^2*y +0.206 x^2 +0.0888 x*y^2 -0.00941 x*y -0.0747 x -0.123 y^3 -0.242 y^2 +0.161 y +0.0496 1
Affine cubic: f(x,y,z) = -0.42 x*z^2 -0.121 y*z^2 +0.22 z^2 -0.17 x^2*z -0.325 x*y*z -0.0938 x*z +0.126 y^2*z -0.104 y*z -0.0762 z -0.642 x^3 +0.125 x^2*y +0.206 x^2 +0.0888 x*y^2 -0.00941 x*y -0.0747 x -0.123 y^3 -0.242 y^2 +0.161 y +0.0496 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].