Random Gaussian cubic surface Seed: 293 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.146 x*z^2 -0.246 y*z^2 -0.058 z^2 +0.342 x^2*z -0.0723 x*y*z -0.101 x*z -0.12 y^2*z -0.0856 y*z +0.0672 z -0.084 x^3 +0.378 x^2*y -0.334 x^2 +0.352 x*y^2 +0.163 x*y -0.112 x -0.279 y^3 -0.408 y^2 +0.198 y -0.219 1
Affine cubic: f(x,y,z) = -0.146 x*z^2 -0.246 y*z^2 -0.058 z^2 +0.342 x^2*z -0.0723 x*y*z -0.101 x*z -0.12 y^2*z -0.0856 y*z +0.0672 z -0.084 x^3 +0.378 x^2*y -0.334 x^2 +0.352 x*y^2 +0.163 x*y -0.112 x -0.279 y^3 -0.408 y^2 +0.198 y -0.219 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].