Random Gaussian cubic surface Seed: 11 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.00974 x*z^2 +0.387 y*z^2 +0.349 z^2 -0.145 x^2*z -0.0849 x*y*z -0.15 x*z +0.162 y^2*z -0.016 y*z +0.213 z -0.526 x^3 +0.446 x^2*y -0.0275 x^2 +0.194 x*y^2 -0.0389 x*y -0.108 x +0.132 y^3 +0.235 y^2 -0.0577 y -0.0435 1
Affine cubic: f(x,y,z) = 0.00974 x*z^2 +0.387 y*z^2 +0.349 z^2 -0.145 x^2*z -0.0849 x*y*z -0.15 x*z +0.162 y^2*z -0.016 y*z +0.213 z -0.526 x^3 +0.446 x^2*y -0.0275 x^2 +0.194 x*y^2 -0.0389 x*y -0.108 x +0.132 y^3 +0.235 y^2 -0.0577 y -0.0435 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].