Random Gaussian cubic surface Seed: 190 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0816 x*z^2 +0.224 y*z^2 -0.107 z^2 -0.159 x^2*z -0.233 x*y*z +0.0199 x*z -0.232 y^2*z +0.439 y*z -0.375 z +0.29 x^3 -0.242 x^2*y +0.0629 x^2 +0.272 x*y^2 +0.192 x*y +0.132 x -0.279 y^3 -0.063 y^2 +0.273 y -0.183 1
Affine cubic: f(x,y,z) = -0.0816 x*z^2 +0.224 y*z^2 -0.107 z^2 -0.159 x^2*z -0.233 x*y*z +0.0199 x*z -0.232 y^2*z +0.439 y*z -0.375 z +0.29 x^3 -0.242 x^2*y +0.0629 x^2 +0.272 x*y^2 +0.192 x*y +0.132 x -0.279 y^3 -0.063 y^2 +0.273 y -0.183 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].