Random Gaussian cubic surface Seed: 344 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.23 x*z^2 -0.0369 y*z^2 -0.116 z^2 -0.452 x^2*z -0.0781 x*y*z +0.25 x*z -0.216 y^2*z +0.228 y*z -0.0989 z -0.136 x^3 +0.651 x^2*y -0.0195 x^2 +0.0881 x*y^2 +0.00464 x*y -0.166 x -0.102 y^3 +0.0363 y^2 +0.246 y -0.0119 1
Affine cubic: f(x,y,z) = -0.23 x*z^2 -0.0369 y*z^2 -0.116 z^2 -0.452 x^2*z -0.0781 x*y*z +0.25 x*z -0.216 y^2*z +0.228 y*z -0.0989 z -0.136 x^3 +0.651 x^2*y -0.0195 x^2 +0.0881 x*y^2 +0.00464 x*y -0.166 x -0.102 y^3 +0.0363 y^2 +0.246 y -0.0119 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].