Random Gaussian cubic surface Seed: 460 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0524 x*z^2 +0.144 y*z^2 -0.0494 z^2 -0.00664 x^2*z -0.255 x*y*z +0.0764 x*z -0.00549 y^2*z -0.106 y*z +0.203 z -0.29 x^3 -0.0557 x^2*y -0.243 x^2 -0.296 x*y^2 -0.289 x*y +0.488 x -0.0796 y^3 +0.389 y^2 -0.355 y +0.105 1
Affine cubic: f(x,y,z) = 0.0524 x*z^2 +0.144 y*z^2 -0.0494 z^2 -0.00664 x^2*z -0.255 x*y*z +0.0764 x*z -0.00549 y^2*z -0.106 y*z +0.203 z -0.29 x^3 -0.0557 x^2*y -0.243 x^2 -0.296 x*y^2 -0.289 x*y +0.488 x -0.0796 y^3 +0.389 y^2 -0.355 y +0.105 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].