Random Gaussian cubic surface Seed: 141 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.284 x*z^2 +0.437 y*z^2 -0.00551 z^2 -0.132 x^2*z -0.136 x*y*z -0.167 x*z +0.0436 y^2*z +0.26 y*z -0.129 z -0.115 x^3 +0.144 x^2*y +0.0121 x^2 +0.303 x*y^2 -0.372 x*y +0.269 x -0.0153 y^3 -0.0992 y^2 -0.478 y +0.0505 1
Affine cubic: f(x,y,z) = -0.284 x*z^2 +0.437 y*z^2 -0.00551 z^2 -0.132 x^2*z -0.136 x*y*z -0.167 x*z +0.0436 y^2*z +0.26 y*z -0.129 z -0.115 x^3 +0.144 x^2*y +0.0121 x^2 +0.303 x*y^2 -0.372 x*y +0.269 x -0.0153 y^3 -0.0992 y^2 -0.478 y +0.0505 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 7 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].