Random Gaussian cubic surface Seed: 378 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.121 x*z^2 -0.0165 y*z^2 +0.0199 z^2 -0.0322 x^2*z +0.383 x*y*z -0.239 x*z -0.36 y^2*z -0.248 y*z -0.0114 z -0.4 x^3 +0.0771 x^2*y -0.435 x^2 -0.00925 x*y^2 -0.154 x*y -0.247 x +0.0447 y^3 +0.106 y^2 +0.208 y -0.304 1
Affine cubic: f(x,y,z) = 0.121 x*z^2 -0.0165 y*z^2 +0.0199 z^2 -0.0322 x^2*z +0.383 x*y*z -0.239 x*z -0.36 y^2*z -0.248 y*z -0.0114 z -0.4 x^3 +0.0771 x^2*y -0.435 x^2 -0.00925 x*y^2 -0.154 x*y -0.247 x +0.0447 y^3 +0.106 y^2 +0.208 y -0.304 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].