Random Gaussian cubic surface Seed: 384 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0985 x*z^2 -0.107 y*z^2 +0.0543 z^2 -0.186 x^2*z -0.18 x*y*z -0.0739 x*z +0.0329 y^2*z +0.608 y*z +0.32 z +0.115 x^3 +0.127 x^2*y +0.192 x^2 -0.106 x*y^2 -0.25 x*y +0.353 x +0.0853 y^3 +0.18 y^2 -0.347 y -0.0673 1
Affine cubic: f(x,y,z) = -0.0985 x*z^2 -0.107 y*z^2 +0.0543 z^2 -0.186 x^2*z -0.18 x*y*z -0.0739 x*z +0.0329 y^2*z +0.608 y*z +0.32 z +0.115 x^3 +0.127 x^2*y +0.192 x^2 -0.106 x*y^2 -0.25 x*y +0.353 x +0.0853 y^3 +0.18 y^2 -0.347 y -0.0673 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].