Random Gaussian cubic surface Seed: 140 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.201 x*z^2 +0.307 y*z^2 -0.202 z^2 +0.422 x^2*z -0.285 x*y*z +0.0737 x*z -0.146 y^2*z -0.237 y*z -0.144 z -0.476 x^3 +0.204 x^2*y +0.0851 x^2 -0.0548 x*y^2 -0.0887 x*y +0.281 x -0.276 y^3 +0.133 y^2 -0.0355 y -0.0271 1
Affine cubic: f(x,y,z) = -0.201 x*z^2 +0.307 y*z^2 -0.202 z^2 +0.422 x^2*z -0.285 x*y*z +0.0737 x*z -0.146 y^2*z -0.237 y*z -0.144 z -0.476 x^3 +0.204 x^2*y +0.0851 x^2 -0.0548 x*y^2 -0.0887 x*y +0.281 x -0.276 y^3 +0.133 y^2 -0.0355 y -0.0271 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].