Random Gaussian cubic surface Seed: 371 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.302 x*z^2 +0.00897 y*z^2 -0.228 z^2 -0.155 x^2*z +0.389 x*y*z +0.033 x*z -0.0582 y^2*z -0.182 y*z +0.1 z +0.253 x^3 -0.211 x^2*y +0.324 x^2 -0.216 x*y^2 -0.086 x*y +0.408 x +0.112 y^3 +0.238 y^2 -0.0637 y -0.354 1
Affine cubic: f(x,y,z) = 0.302 x*z^2 +0.00897 y*z^2 -0.228 z^2 -0.155 x^2*z +0.389 x*y*z +0.033 x*z -0.0582 y^2*z -0.182 y*z +0.1 z +0.253 x^3 -0.211 x^2*y +0.324 x^2 -0.216 x*y^2 -0.086 x*y +0.408 x +0.112 y^3 +0.238 y^2 -0.0637 y -0.354 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].