Random Gaussian cubic surface Seed: 328 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.152 x*z^2 +0.0267 y*z^2 -0.0829 z^2 -0.11 x^2*z +0.294 x*y*z +0.0575 x*z -0.169 y^2*z +0.133 y*z +0.0448 z +0.366 x^3 -0.471 x^2*y -0.13 x^2 +0.0346 x*y^2 +0.458 x*y +0.171 x +0.145 y^3 -0.267 y^2 -0.245 y -0.23 1
Affine cubic: f(x,y,z) = 0.152 x*z^2 +0.0267 y*z^2 -0.0829 z^2 -0.11 x^2*z +0.294 x*y*z +0.0575 x*z -0.169 y^2*z +0.133 y*z +0.0448 z +0.366 x^3 -0.471 x^2*y -0.13 x^2 +0.0346 x*y^2 +0.458 x*y +0.171 x +0.145 y^3 -0.267 y^2 -0.245 y -0.23 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].