Random Gaussian cubic surface Seed: 444 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.206 x*z^2 -0.628 y*z^2 -0.235 z^2 +0.279 x^2*z +0.174 x*y*z +0.21 x*z -0.0709 y^2*z +0.0353 y*z -0.122 z -0.166 x^3 +0.00204 x^2*y -0.149 x^2 -0.0423 x*y^2 +0.14 x*y -0.383 x -0.292 y^3 +0.0379 y^2 -0.17 y -0.044 1
Affine cubic: f(x,y,z) = -0.206 x*z^2 -0.628 y*z^2 -0.235 z^2 +0.279 x^2*z +0.174 x*y*z +0.21 x*z -0.0709 y^2*z +0.0353 y*z -0.122 z -0.166 x^3 +0.00204 x^2*y -0.149 x^2 -0.0423 x*y^2 +0.14 x*y -0.383 x -0.292 y^3 +0.0379 y^2 -0.17 y -0.044 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].