Random Gaussian cubic surface Seed: 40 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.321 x*z^2 -0.3 y*z^2 -0.213 z^2 +0.216 x^2*z -0.292 x*y*z -0.288 x*z -0.11 y^2*z +0.39 y*z -0.258 z -0.196 x^3 +0.0543 x^2*y +0.0406 x^2 +0.108 x*y^2 -0.16 x*y -0.263 x -0.375 y^3 +0.0926 y^2 -0.0583 y +0.12 1
Affine cubic: f(x,y,z) = -0.321 x*z^2 -0.3 y*z^2 -0.213 z^2 +0.216 x^2*z -0.292 x*y*z -0.288 x*z -0.11 y^2*z +0.39 y*z -0.258 z -0.196 x^3 +0.0543 x^2*y +0.0406 x^2 +0.108 x*y^2 -0.16 x*y -0.263 x -0.375 y^3 +0.0926 y^2 -0.0583 y +0.12 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].