Random Gaussian cubic surface Seed: 364 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0825 x*z^2 -0.276 y*z^2 -0.0259 z^2 +0.381 x^2*z +0.116 x*y*z +0.181 x*z -0.152 y^2*z -0.495 y*z -0.124 z -0.0585 x^3 +0.0127 x^2*y -0.257 x^2 +0.14 x*y^2 +0.00382 x*y +0.522 x -0.0985 y^3 +0.096 y^2 +0.189 y +0.158 1
Affine cubic: f(x,y,z) = -0.0825 x*z^2 -0.276 y*z^2 -0.0259 z^2 +0.381 x^2*z +0.116 x*y*z +0.181 x*z -0.152 y^2*z -0.495 y*z -0.124 z -0.0585 x^3 +0.0127 x^2*y -0.257 x^2 +0.14 x*y^2 +0.00382 x*y +0.522 x -0.0985 y^3 +0.096 y^2 +0.189 y +0.158 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].