Random Gaussian cubic surface Seed: 399 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.278 x*z^2 -0.189 y*z^2 -0.207 z^2 -0.148 x^2*z +0.545 x*y*z -0.331 x*z +0.303 y^2*z +0.118 y*z +0.127 z +0.0489 x^3 +0.0168 x^2*y +0.0734 x^2 +0.048 x*y^2 -0.197 x*y -0.0639 x -0.0777 y^3 -0.158 y^2 -0.223 y -0.4 1
Affine cubic: f(x,y,z) = -0.278 x*z^2 -0.189 y*z^2 -0.207 z^2 -0.148 x^2*z +0.545 x*y*z -0.331 x*z +0.303 y^2*z +0.118 y*z +0.127 z +0.0489 x^3 +0.0168 x^2*y +0.0734 x^2 +0.048 x*y^2 -0.197 x*y -0.0639 x -0.0777 y^3 -0.158 y^2 -0.223 y -0.4 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].