Random Gaussian cubic surface Seed: 46 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.14 x*z^2 +0.339 y*z^2 -0.0755 z^2 +0.203 x^2*z -0.326 x*y*z -0.398 x*z -0.00648 y^2*z -0.125 y*z +0.0245 z +0.146 x^3 +0.088 x^2*y -0.0997 x^2 -0.259 x*y^2 -0.293 x*y +0.0657 x +0.478 y^3 -0.00164 y^2 -0.332 y -0.0486 1
Affine cubic: f(x,y,z) = -0.14 x*z^2 +0.339 y*z^2 -0.0755 z^2 +0.203 x^2*z -0.326 x*y*z -0.398 x*z -0.00648 y^2*z -0.125 y*z +0.0245 z +0.146 x^3 +0.088 x^2*y -0.0997 x^2 -0.259 x*y^2 -0.293 x*y +0.0657 x +0.478 y^3 -0.00164 y^2 -0.332 y -0.0486 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].