Random Gaussian cubic surface Seed: 151 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.451 x*z^2 -0.258 y*z^2 -0.257 z^2 +0.289 x^2*z -0.376 x*y*z +0.229 x*z +0.0299 y^2*z -0.0457 y*z +0.105 z -0.383 x^3 +0.0318 x^2*y +0.242 x^2 +0.266 x*y^2 -0.116 x*y +0.154 x +0.181 y^3 -0.0966 y^2 +0.0752 y +0.103 1
Affine cubic: f(x,y,z) = -0.451 x*z^2 -0.258 y*z^2 -0.257 z^2 +0.289 x^2*z -0.376 x*y*z +0.229 x*z +0.0299 y^2*z -0.0457 y*z +0.105 z -0.383 x^3 +0.0318 x^2*y +0.242 x^2 +0.266 x*y^2 -0.116 x*y +0.154 x +0.181 y^3 -0.0966 y^2 +0.0752 y +0.103 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].