Random Gaussian cubic surface Seed: 102 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.121 x*z^2 +0.419 y*z^2 +0.185 z^2 -0.209 x^2*z -0.115 x*y*z +0.167 x*z -0.0085 y^2*z +0.231 y*z -0.376 z +0.409 x^3 +0.365 x^2*y -0.28 x^2 -0.0572 x*y^2 -0.117 x*y -0.0714 x +0.193 y^3 -0.0941 y^2 -0.172 y +0.146 1
Affine cubic: f(x,y,z) = 0.121 x*z^2 +0.419 y*z^2 +0.185 z^2 -0.209 x^2*z -0.115 x*y*z +0.167 x*z -0.0085 y^2*z +0.231 y*z -0.376 z +0.409 x^3 +0.365 x^2*y -0.28 x^2 -0.0572 x*y^2 -0.117 x*y -0.0714 x +0.193 y^3 -0.0941 y^2 -0.172 y +0.146 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].