Random Gaussian cubic surface Seed: 385 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.179 x*z^2 +0.206 y*z^2 +0.0975 z^2 +0.384 x^2*z -0.242 x*y*z -0.134 x*z +0.0478 y^2*z +0.0871 y*z +0.359 z +0.239 x^3 -0.141 x^2*y -0.175 x^2 -0.346 x*y^2 +0.0119 x*y +0.343 x -0.144 y^3 -0.375 y^2 -0.0636 y +0.209 1
Affine cubic: f(x,y,z) = 0.179 x*z^2 +0.206 y*z^2 +0.0975 z^2 +0.384 x^2*z -0.242 x*y*z -0.134 x*z +0.0478 y^2*z +0.0871 y*z +0.359 z +0.239 x^3 -0.141 x^2*y -0.175 x^2 -0.346 x*y^2 +0.0119 x*y +0.343 x -0.144 y^3 -0.375 y^2 -0.0636 y +0.209 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].