Random Gaussian cubic surface Seed: 63 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.132 x*z^2 +0.431 y*z^2 -0.308 z^2 -0.0162 x^2*z +0.229 x*y*z +0.198 x*z +0.261 y^2*z +0.0378 y*z +0.225 z +0.447 x^3 +0.174 x^2*y +0.247 x^2 -0.119 x*y^2 -0.362 x*y -0.0468 x -0.0112 y^3 +0.216 y^2 -0.069 y +0.0211 1
Affine cubic: f(x,y,z) = 0.132 x*z^2 +0.431 y*z^2 -0.308 z^2 -0.0162 x^2*z +0.229 x*y*z +0.198 x*z +0.261 y^2*z +0.0378 y*z +0.225 z +0.447 x^3 +0.174 x^2*y +0.247 x^2 -0.119 x*y^2 -0.362 x*y -0.0468 x -0.0112 y^3 +0.216 y^2 -0.069 y +0.0211 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].