Random Gaussian cubic surface Seed: 85 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.291 x*z^2 -0.25 y*z^2 -0.209 z^2 -0.207 x^2*z -0.0223 x*y*z +0.0867 x*z +0.0974 y^2*z +0.0645 y*z -0.208 z -0.0775 x^3 +0.0441 x^2*y -0.0614 x^2 -0.264 x*y^2 +0.422 x*y -0.102 x -0.308 y^3 -0.191 y^2 -0.246 y -0.489 1
Affine cubic: f(x,y,z) = 0.291 x*z^2 -0.25 y*z^2 -0.209 z^2 -0.207 x^2*z -0.0223 x*y*z +0.0867 x*z +0.0974 y^2*z +0.0645 y*z -0.208 z -0.0775 x^3 +0.0441 x^2*y -0.0614 x^2 -0.264 x*y^2 +0.422 x*y -0.102 x -0.308 y^3 -0.191 y^2 -0.246 y -0.489 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].