Random Gaussian cubic surface Seed: 334 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.124 x*z^2 +0.0711 y*z^2 -0.219 z^2 -0.32 x^2*z -0.29 x*y*z -0.111 x*z -0.275 y^2*z -0.289 y*z +0.135 z +0.0499 x^3 +0.00902 x^2*y -0.0184 x^2 +0.214 x*y^2 -0.115 x*y +0.035 x +0.0889 y^3 -0.437 y^2 +0.241 y -0.485 1
Affine cubic: f(x,y,z) = 0.124 x*z^2 +0.0711 y*z^2 -0.219 z^2 -0.32 x^2*z -0.29 x*y*z -0.111 x*z -0.275 y^2*z -0.289 y*z +0.135 z +0.0499 x^3 +0.00902 x^2*y -0.0184 x^2 +0.214 x*y^2 -0.115 x*y +0.035 x +0.0889 y^3 -0.437 y^2 +0.241 y -0.485 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].