Random Gaussian cubic surface Seed: 483 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.414 x*z^2 +0.224 y*z^2 +0.161 z^2 -0.514 x^2*z -0.202 x*y*z -0.278 x*z -0.0581 y^2*z -0.0567 y*z +0.185 z -0.0143 x^3 -0.375 x^2*y +0.194 x^2 -0.169 x*y^2 -0.0556 x*y +0.269 x -0.0073 y^3 -0.0709 y^2 +0.146 y -0.142 1
Affine cubic: f(x,y,z) = 0.414 x*z^2 +0.224 y*z^2 +0.161 z^2 -0.514 x^2*z -0.202 x*y*z -0.278 x*z -0.0581 y^2*z -0.0567 y*z +0.185 z -0.0143 x^3 -0.375 x^2*y +0.194 x^2 -0.169 x*y^2 -0.0556 x*y +0.269 x -0.0073 y^3 -0.0709 y^2 +0.146 y -0.142 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].