Random Gaussian cubic surface Seed: 55 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.155 x*z^2 -0.549 y*z^2 -0.0562 z^2 +0.267 x^2*z -0.229 x*y*z +0.00981 x*z +0.276 y^2*z -0.215 y*z +0.149 z +0.35 x^3 +0.0824 x^2*y +0.3 x^2 -0.0255 x*y^2 -0.0776 x*y +0.0859 x -0.265 y^3 +0.205 y^2 +0.00821 y -0.238 1
Affine cubic: f(x,y,z) = 0.155 x*z^2 -0.549 y*z^2 -0.0562 z^2 +0.267 x^2*z -0.229 x*y*z +0.00981 x*z +0.276 y^2*z -0.215 y*z +0.149 z +0.35 x^3 +0.0824 x^2*y +0.3 x^2 -0.0255 x*y^2 -0.0776 x*y +0.0859 x -0.265 y^3 +0.205 y^2 +0.00821 y -0.238 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].