Random Gaussian cubic surface Seed: 497 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.388 x*z^2 +0.00495 y*z^2 +0.262 z^2 -0.0973 x^2*z -0.237 x*y*z +0.123 x*z +0.174 y^2*z +0.536 y*z +0.0912 z +0.257 x^3 +0.266 x^2*y +0.00333 x^2 +0.0268 x*y^2 +0.139 x*y +0.169 x -0.0253 y^3 -0.344 y^2 +0.225 y -0.137 1
Affine cubic: f(x,y,z) = 0.388 x*z^2 +0.00495 y*z^2 +0.262 z^2 -0.0973 x^2*z -0.237 x*y*z +0.123 x*z +0.174 y^2*z +0.536 y*z +0.0912 z +0.257 x^3 +0.266 x^2*y +0.00333 x^2 +0.0268 x*y^2 +0.139 x*y +0.169 x -0.0253 y^3 -0.344 y^2 +0.225 y -0.137 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].