Random Gaussian cubic surface Seed: 6 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.208 x*z^2 +0.351 y*z^2 -0.504 z^2 -0.0273 x^2*z +0.2 x*y*z +0.267 x*z +0.129 y^2*z +0.296 y*z +0.0573 z +0.109 x^3 +0.0353 x^2*y -0.212 x^2 -0.167 x*y^2 +0.075 x*y -0.115 x +0.251 y^3 +0.255 y^2 +0.355 y -0.00515 1
Affine cubic: f(x,y,z) = 0.208 x*z^2 +0.351 y*z^2 -0.504 z^2 -0.0273 x^2*z +0.2 x*y*z +0.267 x*z +0.129 y^2*z +0.296 y*z +0.0573 z +0.109 x^3 +0.0353 x^2*y -0.212 x^2 -0.167 x*y^2 +0.075 x*y -0.115 x +0.251 y^3 +0.255 y^2 +0.355 y -0.00515 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].