Random Gaussian cubic surface Seed: 2 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0492 x*z^2 -0.136 y*z^2 -0.107 z^2 -0.635 x^2*z +0.468 x*y*z +0.298 x*z -0.0847 y^2*z +0.201 y*z +0.0732 z -0.144 x^3 +0.254 x^2*y -0.0808 x^2 -0.0856 x*y^2 -0.206 x*y +0.118 x -0.0258 y^3 +0.142 y^2 -0.158 y +0.033 1
Affine cubic: f(x,y,z) = 0.0492 x*z^2 -0.136 y*z^2 -0.107 z^2 -0.635 x^2*z +0.468 x*y*z +0.298 x*z -0.0847 y^2*z +0.201 y*z +0.0732 z -0.144 x^3 +0.254 x^2*y -0.0808 x^2 -0.0856 x*y^2 -0.206 x*y +0.118 x -0.0258 y^3 +0.142 y^2 -0.158 y +0.033 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].