Random Gaussian cubic surface Seed: 44 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.487 x*z^2 +0.0345 y*z^2 +0.11 z^2 +0.383 x^2*z +0.278 x*y*z +0.195 x*z -0.128 y^2*z -0.343 y*z +0.127 z -0.173 x^3 +0.279 x^2*y +0.0712 x^2 -0.251 x*y^2 +0.0903 x*y +0.239 x +0.0598 y^3 -0.264 y^2 +0.0884 y +0.12 1
Affine cubic: f(x,y,z) = 0.487 x*z^2 +0.0345 y*z^2 +0.11 z^2 +0.383 x^2*z +0.278 x*y*z +0.195 x*z -0.128 y^2*z -0.343 y*z +0.127 z -0.173 x^3 +0.279 x^2*y +0.0712 x^2 -0.251 x*y^2 +0.0903 x*y +0.239 x +0.0598 y^3 -0.264 y^2 +0.0884 y +0.12 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].