Random Gaussian cubic surface Seed: 170 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0686 x*z^2 +0.345 y*z^2 -0.144 z^2 +0.53 x^2*z +0.286 x*y*z +0.032 x*z +0.181 y^2*z +0.0834 y*z +0.0582 z -0.322 x^3 +0.0832 x^2*y +0.199 x^2 -0.285 x*y^2 +0.378 x*y -0.152 x -0.19 y^3 -0.000328 y^2 -0.0367 y +0.116 1
Affine cubic: f(x,y,z) = -0.0686 x*z^2 +0.345 y*z^2 -0.144 z^2 +0.53 x^2*z +0.286 x*y*z +0.032 x*z +0.181 y^2*z +0.0834 y*z +0.0582 z -0.322 x^3 +0.0832 x^2*y +0.199 x^2 -0.285 x*y^2 +0.378 x*y -0.152 x -0.19 y^3 -0.000328 y^2 -0.0367 y +0.116 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].