Random Gaussian cubic surface Seed: 319 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.352 x*z^2 -0.452 y*z^2 +0.159 z^2 +0.158 x^2*z -0.363 x*y*z +0.485 x*z -0.114 y^2*z +0.114 y*z +0.0957 z -0.14 x^3 -0.244 x^2*y -0.148 x^2 +0.255 x*y^2 -0.13 x*y -0.129 x -0.00327 y^3 -0.1 y^2 +0.0945 y +0.018 1
Affine cubic: f(x,y,z) = 0.352 x*z^2 -0.452 y*z^2 +0.159 z^2 +0.158 x^2*z -0.363 x*y*z +0.485 x*z -0.114 y^2*z +0.114 y*z +0.0957 z -0.14 x^3 -0.244 x^2*y -0.148 x^2 +0.255 x*y^2 -0.13 x*y -0.129 x -0.00327 y^3 -0.1 y^2 +0.0945 y +0.018 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].