Random Gaussian cubic surface Seed: 332 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0142 x*z^2 +0.0396 y*z^2 -0.073 z^2 +0.121 x^2*z -0.0736 x*y*z -0.145 x*z -0.4 y^2*z -0.264 y*z +0.426 z +0.243 x^3 +0.169 x^2*y -0.00927 x^2 +0.161 x*y^2 +0.114 x*y +0.16 x -0.446 y^3 +0.286 y^2 -0.285 y -0.16 1
Affine cubic: f(x,y,z) = -0.0142 x*z^2 +0.0396 y*z^2 -0.073 z^2 +0.121 x^2*z -0.0736 x*y*z -0.145 x*z -0.4 y^2*z -0.264 y*z +0.426 z +0.243 x^3 +0.169 x^2*y -0.00927 x^2 +0.161 x*y^2 +0.114 x*y +0.16 x -0.446 y^3 +0.286 y^2 -0.285 y -0.16 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].