Random Gaussian cubic surface Seed: 263 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.38 x*z^2 +0.586 y*z^2 +0.207 z^2 +0.204 x^2*z +0.101 x*y*z +0.0888 x*z +0.0713 y^2*z +0.101 y*z -0.14 z +0.107 x^3 -0.0494 x^2*y -0.0625 x^2 -0.2 x*y^2 +0.506 x*y -0.0172 x +0.0601 y^3 +0.118 y^2 +0.105 y -0.18 1
Affine cubic: f(x,y,z) = -0.38 x*z^2 +0.586 y*z^2 +0.207 z^2 +0.204 x^2*z +0.101 x*y*z +0.0888 x*z +0.0713 y^2*z +0.101 y*z -0.14 z +0.107 x^3 -0.0494 x^2*y -0.0625 x^2 -0.2 x*y^2 +0.506 x*y -0.0172 x +0.0601 y^3 +0.118 y^2 +0.105 y -0.18 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].