Random Gaussian cubic surface Seed: 465 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0433 x*z^2 +0.189 y*z^2 +0.668 z^2 +0.176 x^2*z -0.252 x*y*z +0.0559 x*z +0.163 y^2*z -0.0298 y*z +0.378 z +0.0887 x^3 +0.0876 x^2*y +0.0438 x^2 +0.023 x*y^2 +0.0598 x*y +0.21 x -0.35 y^3 -0.0222 y^2 +0.069 y +0.234 1
Affine cubic: f(x,y,z) = -0.0433 x*z^2 +0.189 y*z^2 +0.668 z^2 +0.176 x^2*z -0.252 x*y*z +0.0559 x*z +0.163 y^2*z -0.0298 y*z +0.378 z +0.0887 x^3 +0.0876 x^2*y +0.0438 x^2 +0.023 x*y^2 +0.0598 x*y +0.21 x -0.35 y^3 -0.0222 y^2 +0.069 y +0.234 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 3 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].