Random Gaussian cubic surface Seed: 488 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0522 x*z^2 -0.0411 y*z^2 -0.0292 z^2 +0.378 x^2*z -0.445 x*y*z -0.026 x*z +0.307 y^2*z -0.29 y*z +0.158 z +0.275 x^3 -0.127 x^2*y -0.0295 x^2 -0.0223 x*y^2 +0.264 x*y -0.0608 x +0.0346 y^3 +0.412 y^2 -0.28 y +0.183 1
Affine cubic: f(x,y,z) = 0.0522 x*z^2 -0.0411 y*z^2 -0.0292 z^2 +0.378 x^2*z -0.445 x*y*z -0.026 x*z +0.307 y^2*z -0.29 y*z +0.158 z +0.275 x^3 -0.127 x^2*y -0.0295 x^2 -0.0223 x*y^2 +0.264 x*y -0.0608 x +0.0346 y^3 +0.412 y^2 -0.28 y +0.183 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].