Random Gaussian cubic surface Seed: 467 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0515 x*z^2 +0.3 y*z^2 +0.0641 z^2 +0.0209 x^2*z +0.359 x*y*z -0.141 x*z +0.0778 y^2*z -0.101 y*z +0.238 z +0.248 x^3 -0.389 x^2*y -0.196 x^2 +0.339 x*y^2 +0.0745 x*y -0.069 x -0.422 y^3 +0.13 y^2 -0.0741 y +0.323 1
Affine cubic: f(x,y,z) = 0.0515 x*z^2 +0.3 y*z^2 +0.0641 z^2 +0.0209 x^2*z +0.359 x*y*z -0.141 x*z +0.0778 y^2*z -0.101 y*z +0.238 z +0.248 x^3 -0.389 x^2*y -0.196 x^2 +0.339 x*y^2 +0.0745 x*y -0.069 x -0.422 y^3 +0.13 y^2 -0.0741 y +0.323 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].