Random Gaussian cubic surface Seed: 487 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0938 x*z^2 +0.227 y*z^2 -0.0106 z^2 -0.166 x^2*z -0.347 x*y*z +0.497 x*z -0.245 y^2*z -0.136 y*z +0.0824 z +0.0779 x^3 +0.248 x^2*y +0.0241 x^2 -0.0701 x*y^2 -0.0533 x*y +0.0643 x +0.157 y^3 -0.455 y^2 -0.377 y +0.0683 1
Affine cubic: f(x,y,z) = 0.0938 x*z^2 +0.227 y*z^2 -0.0106 z^2 -0.166 x^2*z -0.347 x*y*z +0.497 x*z -0.245 y^2*z -0.136 y*z +0.0824 z +0.0779 x^3 +0.248 x^2*y +0.0241 x^2 -0.0701 x*y^2 -0.0533 x*y +0.0643 x +0.157 y^3 -0.455 y^2 -0.377 y +0.0683 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].