Random Gaussian cubic surface Seed: 81 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.147 x*z^2 +0.202 y*z^2 -0.187 z^2 +0.131 x^2*z +0.321 x*y*z +0.0117 x*z +0.349 y^2*z +0.299 y*z -0.0645 z +0.174 x^3 +0.153 x^2*y +0.358 x^2 +0.0835 x*y^2 -0.474 x*y +0.106 x +0.181 y^3 +0.0465 y^2 +0.148 y -0.293 1
Affine cubic: f(x,y,z) = 0.147 x*z^2 +0.202 y*z^2 -0.187 z^2 +0.131 x^2*z +0.321 x*y*z +0.0117 x*z +0.349 y^2*z +0.299 y*z -0.0645 z +0.174 x^3 +0.153 x^2*y +0.358 x^2 +0.0835 x*y^2 -0.474 x*y +0.106 x +0.181 y^3 +0.0465 y^2 +0.148 y -0.293 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].