Random Gaussian cubic surface Seed: 278 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.186 x*z^2 -0.0127 y*z^2 -0.0628 z^2 -0.142 x^2*z -0.0253 x*y*z +0.157 x*z -0.356 y^2*z -0.352 y*z +0.0855 z -0.252 x^3 +0.0511 x^2*y +0.318 x^2 +0.104 x*y^2 +0.0827 x*y +0.151 x -0.0228 y^3 -0.564 y^2 -0.309 y -0.191 1
Affine cubic: f(x,y,z) = 0.186 x*z^2 -0.0127 y*z^2 -0.0628 z^2 -0.142 x^2*z -0.0253 x*y*z +0.157 x*z -0.356 y^2*z -0.352 y*z +0.0855 z -0.252 x^3 +0.0511 x^2*y +0.318 x^2 +0.104 x*y^2 +0.0827 x*y +0.151 x -0.0228 y^3 -0.564 y^2 -0.309 y -0.191 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 7 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].