Random Gaussian cubic surface Seed: 66 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.155 x*z^2 -0.154 y*z^2 -0.141 z^2 -0.303 x^2*z -0.379 x*y*z -0.444 x*z +0.143 y^2*z +0.32 y*z +0.126 z +0.0816 x^3 +0.0838 x^2*y -0.0359 x^2 +0.278 x*y^2 -0.222 x*y +0.306 x -0.0448 y^3 -0.0158 y^2 -0.35 y +0.0229 1
Affine cubic: f(x,y,z) = 0.155 x*z^2 -0.154 y*z^2 -0.141 z^2 -0.303 x^2*z -0.379 x*y*z -0.444 x*z +0.143 y^2*z +0.32 y*z +0.126 z +0.0816 x^3 +0.0838 x^2*y -0.0359 x^2 +0.278 x*y^2 -0.222 x*y +0.306 x -0.0448 y^3 -0.0158 y^2 -0.35 y +0.0229 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].