Random Gaussian cubic surface Seed: 300 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0963 x*z^2 -0.319 y*z^2 -0.0172 z^2 -0.00838 x^2*z -0.0257 x*y*z -0.241 x*z -0.334 y^2*z -0.263 y*z +0.0801 z -0.0984 x^3 -0.24 x^2*y -0.286 x^2 +0.245 x*y^2 +0.0301 x*y +0.232 x +0.0895 y^3 -0.591 y^2 +0.0281 y +0.146 1
Affine cubic: f(x,y,z) = -0.0963 x*z^2 -0.319 y*z^2 -0.0172 z^2 -0.00838 x^2*z -0.0257 x*y*z -0.241 x*z -0.334 y^2*z -0.263 y*z +0.0801 z -0.0984 x^3 -0.24 x^2*y -0.286 x^2 +0.245 x*y^2 +0.0301 x*y +0.232 x +0.0895 y^3 -0.591 y^2 +0.0281 y +0.146 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 15 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].