Random Gaussian cubic surface Seed: 349 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.232 x*z^2 +0.179 y*z^2 -0.0634 z^2 +0.159 x^2*z -0.0845 x*y*z +0.0736 x*z -0.249 y^2*z +0.449 y*z +0.0248 z -0.249 x^3 +0.128 x^2*y +0.0634 x^2 +0.382 x*y^2 -0.0826 x*y +0.0753 x -0.413 y^3 -0.226 y^2 -0.376 y -0.0653 1
Affine cubic: f(x,y,z) = -0.232 x*z^2 +0.179 y*z^2 -0.0634 z^2 +0.159 x^2*z -0.0845 x*y*z +0.0736 x*z -0.249 y^2*z +0.449 y*z +0.0248 z -0.249 x^3 +0.128 x^2*y +0.0634 x^2 +0.382 x*y^2 -0.0826 x*y +0.0753 x -0.413 y^3 -0.226 y^2 -0.376 y -0.0653 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].