Random Gaussian cubic surface Seed: 155 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0851 x*z^2 -0.285 y*z^2 -0.085 z^2 +0.0213 x^2*z +0.373 x*y*z -0.563 x*z +0.164 y^2*z +0.179 y*z +0.2 z -0.189 x^3 -0.0833 x^2*y -0.0209 x^2 -0.328 x*y^2 -0.131 x*y +0.111 x +0.158 y^3 -0.374 y^2 -0.0503 y +0.0381 1
Affine cubic: f(x,y,z) = 0.0851 x*z^2 -0.285 y*z^2 -0.085 z^2 +0.0213 x^2*z +0.373 x*y*z -0.563 x*z +0.164 y^2*z +0.179 y*z +0.2 z -0.189 x^3 -0.0833 x^2*y -0.0209 x^2 -0.328 x*y^2 -0.131 x*y +0.111 x +0.158 y^3 -0.374 y^2 -0.0503 y +0.0381 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 7 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].