Random Gaussian cubic surface Seed: 195 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.127 x*z^2 +0.279 y*z^2 -0.0155 z^2 -0.335 x^2*z +0.201 x*y*z +0.116 x*z +0.0775 y^2*z -0.118 y*z -0.0365 z +0.173 x^3 +0.00983 x^2*y +0.206 x^2 +0.61 x*y^2 -0.256 x*y -0.204 x -0.257 y^3 -0.163 y^2 +0.264 y -0.0606 1
Affine cubic: f(x,y,z) = 0.127 x*z^2 +0.279 y*z^2 -0.0155 z^2 -0.335 x^2*z +0.201 x*y*z +0.116 x*z +0.0775 y^2*z -0.118 y*z -0.0365 z +0.173 x^3 +0.00983 x^2*y +0.206 x^2 +0.61 x*y^2 -0.256 x*y -0.204 x -0.257 y^3 -0.163 y^2 +0.264 y -0.0606 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].