Random Gaussian cubic surface Seed: 337 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0646 x*z^2 -0.18 y*z^2 -0.068 z^2 -0.0791 x^2*z +0.714 x*y*z +0.126 x*z -0.0212 y^2*z -0.0678 y*z +0.0964 z -0.105 x^3 -0.0764 x^2*y +0.112 x^2 -0.241 x*y^2 -0.165 x*y +0.258 x -0.374 y^3 -0.212 y^2 -0.106 y +0.186 1
Affine cubic: f(x,y,z) = 0.0646 x*z^2 -0.18 y*z^2 -0.068 z^2 -0.0791 x^2*z +0.714 x*y*z +0.126 x*z -0.0212 y^2*z -0.0678 y*z +0.0964 z -0.105 x^3 -0.0764 x^2*y +0.112 x^2 -0.241 x*y^2 -0.165 x*y +0.258 x -0.374 y^3 -0.212 y^2 -0.106 y +0.186 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].