Random Gaussian cubic surface Seed: 434 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.295 x*z^2 +0.158 y*z^2 -0.418 z^2 -0.322 x^2*z +0.0122 x*y*z +0.206 x*z +0.367 y^2*z +0.211 y*z +0.276 z -0.27 x^3 -0.296 x^2*y -0.0917 x^2 +0.0513 x*y^2 -0.32 x*y -0.0248 x -0.056 y^3 +0.0393 y^2 +0.103 y -0.149 1
Affine cubic: f(x,y,z) = -0.295 x*z^2 +0.158 y*z^2 -0.418 z^2 -0.322 x^2*z +0.0122 x*y*z +0.206 x*z +0.367 y^2*z +0.211 y*z +0.276 z -0.27 x^3 -0.296 x^2*y -0.0917 x^2 +0.0513 x*y^2 -0.32 x*y -0.0248 x -0.056 y^3 +0.0393 y^2 +0.103 y -0.149 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].