Random Gaussian cubic surface Seed: 77 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0834 x*z^2 -0.111 y*z^2 +0.517 z^2 -0.313 x^2*z +0.129 x*y*z -0.0279 x*z -0.0691 y^2*z +0.208 y*z -0.354 z -0.192 x^3 -0.0222 x^2*y +0.339 x^2 +0.0174 x*y^2 +0.175 x*y -0.363 x -0.241 y^3 +0.189 y^2 -0.122 y -0.0123 1
Affine cubic: f(x,y,z) = 0.0834 x*z^2 -0.111 y*z^2 +0.517 z^2 -0.313 x^2*z +0.129 x*y*z -0.0279 x*z -0.0691 y^2*z +0.208 y*z -0.354 z -0.192 x^3 -0.0222 x^2*y +0.339 x^2 +0.0174 x*y^2 +0.175 x*y -0.363 x -0.241 y^3 +0.189 y^2 -0.122 y -0.0123 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].