Random Gaussian cubic surface Seed: 54 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.186 x*z^2 -0.0377 y*z^2 +0.238 z^2 +0.334 x^2*z -0.0986 x*y*z +0.248 x*z -0.108 y^2*z +0.0103 y*z +0.205 z -0.0628 x^3 +0.454 x^2*y -0.485 x^2 -0.057 x*y^2 -0.155 x*y -0.0448 x +0.0141 y^3 -0.307 y^2 +0.216 y -0.236 1
Affine cubic: f(x,y,z) = -0.186 x*z^2 -0.0377 y*z^2 +0.238 z^2 +0.334 x^2*z -0.0986 x*y*z +0.248 x*z -0.108 y^2*z +0.0103 y*z +0.205 z -0.0628 x^3 +0.454 x^2*y -0.485 x^2 -0.057 x*y^2 -0.155 x*y -0.0448 x +0.0141 y^3 -0.307 y^2 +0.216 y -0.236 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].