Random Gaussian cubic surface Seed: 341 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.292 x*z^2 -0.221 y*z^2 -0.204 z^2 -0.027 x^2*z +0.225 x*y*z +0.118 x*z +0.315 y^2*z +0.136 y*z +0.109 z -0.103 x^3 +0.387 x^2*y +0.174 x^2 +0.00433 x*y^2 +0.338 x*y -0.486 x +0.28 y^3 +0.0883 y^2 -0.00141 y -0.0447 1
Affine cubic: f(x,y,z) = 0.292 x*z^2 -0.221 y*z^2 -0.204 z^2 -0.027 x^2*z +0.225 x*y*z +0.118 x*z +0.315 y^2*z +0.136 y*z +0.109 z -0.103 x^3 +0.387 x^2*y +0.174 x^2 +0.00433 x*y^2 +0.338 x*y -0.486 x +0.28 y^3 +0.0883 y^2 -0.00141 y -0.0447 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].