Random Gaussian cubic surface Seed: 30 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.359 x*z^2 +0.169 y*z^2 -0.221 z^2 -0.0483 x^2*z -0.0653 x*y*z +0.538 x*z -0.215 y^2*z +0.313 y*z +0.0281 z +0.233 x^3 -0.000633 x^2*y +0.0895 x^2 +0.112 x*y^2 +0.025 x*y +0.148 x +0.0796 y^3 +0.281 y^2 +0.412 y -0.0201 1
Affine cubic: f(x,y,z) = 0.359 x*z^2 +0.169 y*z^2 -0.221 z^2 -0.0483 x^2*z -0.0653 x*y*z +0.538 x*z -0.215 y^2*z +0.313 y*z +0.0281 z +0.233 x^3 -0.000633 x^2*y +0.0895 x^2 +0.112 x*y^2 +0.025 x*y +0.148 x +0.0796 y^3 +0.281 y^2 +0.412 y -0.0201 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].