Random Gaussian cubic surface Seed: 124 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0739 x*z^2 -0.142 y*z^2 -0.273 z^2 -0.292 x^2*z +0.2 x*y*z +0.15 x*z -0.253 y^2*z +0.267 y*z -0.123 z +0.275 x^3 -0.3 x^2*y +0.0591 x^2 -0.471 x*y^2 +0.0177 x*y +0.247 x -0.0209 y^3 -0.191 y^2 +0.233 y +0.242 1
Affine cubic: f(x,y,z) = -0.0739 x*z^2 -0.142 y*z^2 -0.273 z^2 -0.292 x^2*z +0.2 x*y*z +0.15 x*z -0.253 y^2*z +0.267 y*z -0.123 z +0.275 x^3 -0.3 x^2*y +0.0591 x^2 -0.471 x*y^2 +0.0177 x*y +0.247 x -0.0209 y^3 -0.191 y^2 +0.233 y +0.242 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].