Random Gaussian cubic surface Seed: 172 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.131 x*z^2 -0.193 y*z^2 +0.284 z^2 -0.189 x^2*z +0.436 x*y*z -0.273 x*z +0.128 y^2*z +0.2 y*z +0.18 z -0.0704 x^3 -0.0525 x^2*y -0.0644 x^2 +0.377 x*y^2 +0.238 x*y -0.0353 x -0.259 y^3 -0.397 y^2 -0.197 y -0.00476 1
Affine cubic: f(x,y,z) = -0.131 x*z^2 -0.193 y*z^2 +0.284 z^2 -0.189 x^2*z +0.436 x*y*z -0.273 x*z +0.128 y^2*z +0.2 y*z +0.18 z -0.0704 x^3 -0.0525 x^2*y -0.0644 x^2 +0.377 x*y^2 +0.238 x*y -0.0353 x -0.259 y^3 -0.397 y^2 -0.197 y -0.00476 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].