Random Gaussian cubic surface Seed: 29 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.115 x*z^2 +0.0147 y*z^2 -0.0487 z^2 -0.0495 x^2*z +0.0184 x*y*z -0.0665 x*z +0.0875 y^2*z -0.0144 y*z +0.167 z -0.194 x^3 -0.106 x^2*y -0.252 x^2 -0.492 x*y^2 -0.658 x*y +0.0177 x -0.245 y^3 -0.222 y^2 -0.171 y +0.123 1
Affine cubic: f(x,y,z) = -0.115 x*z^2 +0.0147 y*z^2 -0.0487 z^2 -0.0495 x^2*z +0.0184 x*y*z -0.0665 x*z +0.0875 y^2*z -0.0144 y*z +0.167 z -0.194 x^3 -0.106 x^2*y -0.252 x^2 -0.492 x*y^2 -0.658 x*y +0.0177 x -0.245 y^3 -0.222 y^2 -0.171 y +0.123 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].