Random Gaussian cubic surface Seed: 219 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.281 x*z^2 -0.132 y*z^2 +0.182 z^2 +0.639 x^2*z -0.254 x*y*z -0.0789 x*z -0.145 y^2*z +0.15 y*z +0.269 z +0.0135 x^3 -0.283 x^2*y -0.0569 x^2 -0.197 x*y^2 +0.249 x*y -0.192 x -0.134 y^3 -0.0474 y^2 +0.182 y -0.043 1
Affine cubic: f(x,y,z) = -0.281 x*z^2 -0.132 y*z^2 +0.182 z^2 +0.639 x^2*z -0.254 x*y*z -0.0789 x*z -0.145 y^2*z +0.15 y*z +0.269 z +0.0135 x^3 -0.283 x^2*y -0.0569 x^2 -0.197 x*y^2 +0.249 x*y -0.192 x -0.134 y^3 -0.0474 y^2 +0.182 y -0.043 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].