Random Gaussian cubic surface Seed: 139 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.193 x*z^2 -0.335 y*z^2 -0.059 z^2 -0.207 x^2*z +0.101 x*y*z +0.224 x*z -0.0365 y^2*z -0.502 y*z -0.379 z +0.0201 x^3 +0.314 x^2*y +0.00119 x^2 -0.0132 x*y^2 +0.309 x*y +0.102 x +0.102 y^3 -0.0462 y^2 +0.209 y +0.292 1
Affine cubic: f(x,y,z) = -0.193 x*z^2 -0.335 y*z^2 -0.059 z^2 -0.207 x^2*z +0.101 x*y*z +0.224 x*z -0.0365 y^2*z -0.502 y*z -0.379 z +0.0201 x^3 +0.314 x^2*y +0.00119 x^2 -0.0132 x*y^2 +0.309 x*y +0.102 x +0.102 y^3 -0.0462 y^2 +0.209 y +0.292 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].