Random Gaussian cubic surface Seed: 52 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.239 x*z^2 +0.0702 y*z^2 -0.0185 z^2 -0.0273 x^2*z +0.0937 x*y*z +0.193 x*z +0.0549 y^2*z +0.0516 y*z -0.329 z +0.167 x^3 -0.0943 x^2*y +0.287 x^2 +0.38 x*y^2 -0.473 x*y +0.385 x -0.197 y^3 -0.3 y^2 -0.0673 y +0.0866 1
Affine cubic: f(x,y,z) = -0.239 x*z^2 +0.0702 y*z^2 -0.0185 z^2 -0.0273 x^2*z +0.0937 x*y*z +0.193 x*z +0.0549 y^2*z +0.0516 y*z -0.329 z +0.167 x^3 -0.0943 x^2*y +0.287 x^2 +0.38 x*y^2 -0.473 x*y +0.385 x -0.197 y^3 -0.3 y^2 -0.0673 y +0.0866 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].