Random Gaussian cubic surface Seed: 301 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0746 x*z^2 -0.301 y*z^2 -0.342 z^2 -0.191 x^2*z -0.0139 x*y*z -0.329 x*z +0.0969 y^2*z -0.0891 y*z -0.0126 z -0.145 x^3 -0.0645 x^2*y -0.0581 x^2 -0.655 x*y^2 +0.15 x*y +0.0111 x -0.116 y^3 +0.31 y^2 +0.0631 y +0.175 1
Affine cubic: f(x,y,z) = 0.0746 x*z^2 -0.301 y*z^2 -0.342 z^2 -0.191 x^2*z -0.0139 x*y*z -0.329 x*z +0.0969 y^2*z -0.0891 y*z -0.0126 z -0.145 x^3 -0.0645 x^2*y -0.0581 x^2 -0.655 x*y^2 +0.15 x*y +0.0111 x -0.116 y^3 +0.31 y^2 +0.0631 y +0.175 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].