Random Gaussian cubic surface Seed: 428 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0328 x*z^2 -0.152 y*z^2 -0.46 z^2 +0.106 x^2*z -0.213 x*y*z -0.248 x*z +0.0316 y^2*z -0.235 y*z +0.0361 z +0.188 x^3 +0.468 x^2*y -0.03 x^2 +0.089 x*y^2 -0.229 x*y +0.231 x +0.313 y^3 -0.19 y^2 +0.0789 y +0.282 1
Affine cubic: f(x,y,z) = 0.0328 x*z^2 -0.152 y*z^2 -0.46 z^2 +0.106 x^2*z -0.213 x*y*z -0.248 x*z +0.0316 y^2*z -0.235 y*z +0.0361 z +0.188 x^3 +0.468 x^2*y -0.03 x^2 +0.089 x*y^2 -0.229 x*y +0.231 x +0.313 y^3 -0.19 y^2 +0.0789 y +0.282 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].