Random Gaussian cubic surface Seed: 317 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.184 x*z^2 -0.133 y*z^2 +0.329 z^2 +0.147 x^2*z +0.0934 x*y*z +0.335 x*z +0.378 y^2*z -0.294 y*z +0.0266 z -0.028 x^3 -0.329 x^2*y +0.217 x^2 -0.179 x*y^2 +0.275 x*y -0.117 x +0.336 y^3 +0.139 y^2 +0.23 y +0.0766 1
Affine cubic: f(x,y,z) = -0.184 x*z^2 -0.133 y*z^2 +0.329 z^2 +0.147 x^2*z +0.0934 x*y*z +0.335 x*z +0.378 y^2*z -0.294 y*z +0.0266 z -0.028 x^3 -0.329 x^2*y +0.217 x^2 -0.179 x*y^2 +0.275 x*y -0.117 x +0.336 y^3 +0.139 y^2 +0.23 y +0.0766 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].