Random Gaussian cubic surface Seed: 156 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0512 x*z^2 +0.0169 y*z^2 -0.272 z^2 -0.383 x^2*z -0.0204 x*y*z +0.0275 x*z +0.16 y^2*z +0.427 y*z +0.398 z -0.31 x^3 -0.349 x^2*y +0.148 x^2 -0.00523 x*y^2 -0.361 x*y +0.097 x +0.0737 y^3 +0.0239 y^2 +0.134 y +0.066 1
Affine cubic: f(x,y,z) = -0.0512 x*z^2 +0.0169 y*z^2 -0.272 z^2 -0.383 x^2*z -0.0204 x*y*z +0.0275 x*z +0.16 y^2*z +0.427 y*z +0.398 z -0.31 x^3 -0.349 x^2*y +0.148 x^2 -0.00523 x*y^2 -0.361 x*y +0.097 x +0.0737 y^3 +0.0239 y^2 +0.134 y +0.066 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].