Random Gaussian cubic surface Seed: 105 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0125 x*z^2 +0.246 y*z^2 +0.391 z^2 -0.0105 x^2*z -0.0471 x*y*z +0.209 x*z +0.0115 y^2*z +0.16 y*z +0.315 z +0.11 x^3 +0.214 x^2*y -0.459 x^2 +0.207 x*y^2 -0.0312 x*y -0.184 x -0.0286 y^3 -0.233 y^2 -0.23 y -0.401 1
Affine cubic: f(x,y,z) = -0.0125 x*z^2 +0.246 y*z^2 +0.391 z^2 -0.0105 x^2*z -0.0471 x*y*z +0.209 x*z +0.0115 y^2*z +0.16 y*z +0.315 z +0.11 x^3 +0.214 x^2*y -0.459 x^2 +0.207 x*y^2 -0.0312 x*y -0.184 x -0.0286 y^3 -0.233 y^2 -0.23 y -0.401 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].