Random Gaussian cubic surface Seed: 282 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.408 x*z^2 -0.469 y*z^2 -0.402 z^2 -0.329 x^2*z -0.0207 x*y*z +0.00847 x*z +0.00727 y^2*z -0.0523 y*z -0.0141 z -0.124 x^3 -0.0731 x^2*y +0.245 x^2 -0.176 x*y^2 +0.146 x*y +0.0307 x -0.0747 y^3 -0.419 y^2 -0.0195 y +0.157 1
Affine cubic: f(x,y,z) = 0.408 x*z^2 -0.469 y*z^2 -0.402 z^2 -0.329 x^2*z -0.0207 x*y*z +0.00847 x*z +0.00727 y^2*z -0.0523 y*z -0.0141 z -0.124 x^3 -0.0731 x^2*y +0.245 x^2 -0.176 x*y^2 +0.146 x*y +0.0307 x -0.0747 y^3 -0.419 y^2 -0.0195 y +0.157 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 15 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].