Random Gaussian cubic surface Seed: 115 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.253 x*z^2 -0.483 y*z^2 -0.179 z^2 +0.228 x^2*z +0.00297 x*y*z -0.221 x*z +0.000422 y^2*z -0.0564 y*z -0.17 z -0.221 x^3 +0.0785 x^2*y -0.114 x^2 -0.64 x*y^2 -0.0167 x*y -0.13 x -0.131 y^3 +0.00996 y^2 -0.156 y +0.0266 1
Affine cubic: f(x,y,z) = 0.253 x*z^2 -0.483 y*z^2 -0.179 z^2 +0.228 x^2*z +0.00297 x*y*z -0.221 x*z +0.000422 y^2*z -0.0564 y*z -0.17 z -0.221 x^3 +0.0785 x^2*y -0.114 x^2 -0.64 x*y^2 -0.0167 x*y -0.13 x -0.131 y^3 +0.00996 y^2 -0.156 y +0.0266 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].