Random Gaussian cubic surface Seed: 185 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.38 x*z^2 +0.0625 y*z^2 +0.228 z^2 -0.0343 x^2*z -0.293 x*y*z -0.0859 x*z +0.0487 y^2*z -0.34 y*z +0.271 z +0.276 x^3 -0.405 x^2*y -0.0322 x^2 +0.119 x*y^2 -0.0798 x*y +0.119 x -0.342 y^3 +0.21 y^2 +0.263 y +0.0881 1
Affine cubic: f(x,y,z) = 0.38 x*z^2 +0.0625 y*z^2 +0.228 z^2 -0.0343 x^2*z -0.293 x*y*z -0.0859 x*z +0.0487 y^2*z -0.34 y*z +0.271 z +0.276 x^3 -0.405 x^2*y -0.0322 x^2 +0.119 x*y^2 -0.0798 x*y +0.119 x -0.342 y^3 +0.21 y^2 +0.263 y +0.0881 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].