Random Gaussian cubic surface Seed: 358 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.479 x*z^2 -0.0739 y*z^2 +0.0659 z^2 +0.201 x^2*z -0.0411 x*y*z -0.0056 x*z -0.171 y^2*z +0.239 y*z +0.0669 z -0.000808 x^3 +0.0839 x^2*y -0.063 x^2 -0.34 x*y^2 +0.412 x*y +0.146 x +0.0805 y^3 +0.433 y^2 -0.341 y +0.0103 1
Affine cubic: f(x,y,z) = 0.479 x*z^2 -0.0739 y*z^2 +0.0659 z^2 +0.201 x^2*z -0.0411 x*y*z -0.0056 x*z -0.171 y^2*z +0.239 y*z +0.0669 z -0.000808 x^3 +0.0839 x^2*y -0.063 x^2 -0.34 x*y^2 +0.412 x*y +0.146 x +0.0805 y^3 +0.433 y^2 -0.341 y +0.0103 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].