Random Gaussian cubic surface Seed: 476 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.248 x*z^2 +0.304 y*z^2 +0.24 z^2 +0.142 x^2*z -0.0972 x*y*z -0.161 x*z +0.412 y^2*z -0.0716 y*z -0.0629 z +0.131 x^3 -0.121 x^2*y -0.0388 x^2 +0.429 x*y^2 +0.228 x*y +0.48 x +0.0981 y^3 +0.024 y^2 +0.151 y +0.146 1
Affine cubic: f(x,y,z) = -0.248 x*z^2 +0.304 y*z^2 +0.24 z^2 +0.142 x^2*z -0.0972 x*y*z -0.161 x*z +0.412 y^2*z -0.0716 y*z -0.0629 z +0.131 x^3 -0.121 x^2*y -0.0388 x^2 +0.429 x*y^2 +0.228 x*y +0.48 x +0.0981 y^3 +0.024 y^2 +0.151 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 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].