Random Gaussian cubic surface Seed: 368 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.166 x*z^2 -0.339 y*z^2 +0.268 z^2 -0.124 x^2*z -0.0733 x*y*z -0.0672 x*z -0.344 y^2*z +0.227 y*z +0.149 z -0.187 x^3 +0.318 x^2*y -0.0261 x^2 +0.551 x*y^2 -0.0536 x*y +0.235 x -0.00155 y^3 +0.249 y^2 -0.0657 y -0.0528 1
Affine cubic: f(x,y,z) = -0.166 x*z^2 -0.339 y*z^2 +0.268 z^2 -0.124 x^2*z -0.0733 x*y*z -0.0672 x*z -0.344 y^2*z +0.227 y*z +0.149 z -0.187 x^3 +0.318 x^2*y -0.0261 x^2 +0.551 x*y^2 -0.0536 x*y +0.235 x -0.00155 y^3 +0.249 y^2 -0.0657 y -0.0528 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].