Random Gaussian cubic surface Seed: 484 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.146 x*z^2 +0.185 y*z^2 -0.000221 z^2 -0.311 x^2*z -0.43 x*y*z +0.0884 x*z -0.258 y^2*z -0.226 y*z -0.119 z -0.0848 x^3 +0.0122 x^2*y +0.106 x^2 -0.16 x*y^2 +0.406 x*y +0.221 x -0.381 y^3 -0.342 y^2 -0.0474 y -0.0101 1
Affine cubic: f(x,y,z) = 0.146 x*z^2 +0.185 y*z^2 -0.000221 z^2 -0.311 x^2*z -0.43 x*y*z +0.0884 x*z -0.258 y^2*z -0.226 y*z -0.119 z -0.0848 x^3 +0.0122 x^2*y +0.106 x^2 -0.16 x*y^2 +0.406 x*y +0.221 x -0.381 y^3 -0.342 y^2 -0.0474 y -0.0101 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].