Random Gaussian cubic surface Seed: 330 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.401 x*z^2 +0.242 y*z^2 +0.247 z^2 +0.0933 x^2*z +0.237 x*y*z +0.179 x*z -0.202 y^2*z +0.146 y*z +0.22 z +0.164 x^3 -0.103 x^2*y -0.000205 x^2 +0.265 x*y^2 +0.054 x*y +0.127 x -0.0212 y^3 +0.234 y^2 -0.327 y +0.474 1
Affine cubic: f(x,y,z) = 0.401 x*z^2 +0.242 y*z^2 +0.247 z^2 +0.0933 x^2*z +0.237 x*y*z +0.179 x*z -0.202 y^2*z +0.146 y*z +0.22 z +0.164 x^3 -0.103 x^2*y -0.000205 x^2 +0.265 x*y^2 +0.054 x*y +0.127 x -0.0212 y^3 +0.234 y^2 -0.327 y +0.474 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].