Random Gaussian cubic surface Seed: 453 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.321 x*z^2 -0.304 y*z^2 -0.223 z^2 -0.287 x^2*z -0.221 x*y*z +0.317 x*z -0.197 y^2*z +0.0654 y*z -0.108 z -0.025 x^3 -0.164 x^2*y +0.0579 x^2 -0.0958 x*y^2 +0.166 x*y -0.171 x -0.217 y^3 +0.0257 y^2 +0.399 y -0.405 1
Affine cubic: f(x,y,z) = 0.321 x*z^2 -0.304 y*z^2 -0.223 z^2 -0.287 x^2*z -0.221 x*y*z +0.317 x*z -0.197 y^2*z +0.0654 y*z -0.108 z -0.025 x^3 -0.164 x^2*y +0.0579 x^2 -0.0958 x*y^2 +0.166 x*y -0.171 x -0.217 y^3 +0.0257 y^2 +0.399 y -0.405 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].