Random Gaussian cubic surface Seed: 68 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.414 x*z^2 +0.191 y*z^2 +0.157 z^2 +0.00318 x^2*z +0.293 x*y*z +0.179 x*z +0.00893 y^2*z +0.0715 y*z -0.329 z +0.187 x^3 +0.119 x^2*y -0.454 x^2 +0.314 x*y^2 +0.155 x*y +0.148 x -0.0123 y^3 -0.175 y^2 +0.303 y +0.118 1
Affine cubic: f(x,y,z) = 0.414 x*z^2 +0.191 y*z^2 +0.157 z^2 +0.00318 x^2*z +0.293 x*y*z +0.179 x*z +0.00893 y^2*z +0.0715 y*z -0.329 z +0.187 x^3 +0.119 x^2*y -0.454 x^2 +0.314 x*y^2 +0.155 x*y +0.148 x -0.0123 y^3 -0.175 y^2 +0.303 y +0.118 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].