Random Gaussian cubic surface Seed: 4 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.131 x*z^2 -0.0352 y*z^2 +0.335 z^2 +0.133 x^2*z -0.331 x*y*z -0.00105 x*z -0.126 y^2*z +0.03 y*z -0.324 z +0.0487 x^3 +0.0475 x^2*y +0.318 x^2 +0.0638 x*y^2 +0.103 x*y -0.301 x +0.454 y^3 -0.386 y^2 +0.222 y -0.0665 1
Affine cubic: f(x,y,z) = -0.131 x*z^2 -0.0352 y*z^2 +0.335 z^2 +0.133 x^2*z -0.331 x*y*z -0.00105 x*z -0.126 y^2*z +0.03 y*z -0.324 z +0.0487 x^3 +0.0475 x^2*y +0.318 x^2 +0.0638 x*y^2 +0.103 x*y -0.301 x +0.454 y^3 -0.386 y^2 +0.222 y -0.0665 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].