Random Gaussian cubic surface Seed: 215 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0874 x*z^2 -0.0919 y*z^2 -0.0496 z^2 +0.0971 x^2*z -0.281 x*y*z -0.502 x*z -0.00374 y^2*z -0.309 y*z -0.124 z +0.331 x^3 -0.197 x^2*y -0.0129 x^2 +0.156 x*y^2 +0.13 x*y +0.144 x +0.0362 y^3 +0.399 y^2 +0.0514 y -0.396 1
Affine cubic: f(x,y,z) = 0.0874 x*z^2 -0.0919 y*z^2 -0.0496 z^2 +0.0971 x^2*z -0.281 x*y*z -0.502 x*z -0.00374 y^2*z -0.309 y*z -0.124 z +0.331 x^3 -0.197 x^2*y -0.0129 x^2 +0.156 x*y^2 +0.13 x*y +0.144 x +0.0362 y^3 +0.399 y^2 +0.0514 y -0.396 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].