Random Gaussian cubic surface Seed: 288 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.247 x*z^2 +0.171 y*z^2 +0.126 z^2 +0.00308 x^2*z +0.322 x*y*z +0.546 x*z -0.00314 y^2*z +0.0856 y*z -0.061 z -0.289 x^3 +0.149 x^2*y -0.069 x^2 +0.43 x*y^2 -0.113 x*y -0.000809 x -0.252 y^3 +0.0456 y^2 +0.191 y +0.265 1
Affine cubic: f(x,y,z) = 0.247 x*z^2 +0.171 y*z^2 +0.126 z^2 +0.00308 x^2*z +0.322 x*y*z +0.546 x*z -0.00314 y^2*z +0.0856 y*z -0.061 z -0.289 x^3 +0.149 x^2*y -0.069 x^2 +0.43 x*y^2 -0.113 x*y -0.000809 x -0.252 y^3 +0.0456 y^2 +0.191 y +0.265 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].