Random Gaussian cubic surface Seed: 162 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.134 x*z^2 -0.0838 y*z^2 +0.0739 z^2 -0.329 x^2*z +0.0263 x*y*z +0.231 x*z +0.105 y^2*z +0.449 y*z +0.225 z -0.287 x^3 -0.344 x^2*y +0.0273 x^2 -0.108 x*y^2 -0.102 x*y +0.145 x -0.0737 y^3 -0.537 y^2 +0.0185 y +0.0605 1
Affine cubic: f(x,y,z) = 0.134 x*z^2 -0.0838 y*z^2 +0.0739 z^2 -0.329 x^2*z +0.0263 x*y*z +0.231 x*z +0.105 y^2*z +0.449 y*z +0.225 z -0.287 x^3 -0.344 x^2*y +0.0273 x^2 -0.108 x*y^2 -0.102 x*y +0.145 x -0.0737 y^3 -0.537 y^2 +0.0185 y +0.0605 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 15 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].