Random Gaussian cubic surface Seed: 459 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.158 x*z^2 -0.0655 y*z^2 +0.197 z^2 +0.0421 x^2*z -0.017 x*y*z -0.0187 x*z -0.188 y^2*z +0.174 y*z +0.164 z -0.611 x^3 -0.336 x^2*y -0.0692 x^2 -0.217 x*y^2 -0.0998 x*y -0.0153 x -0.169 y^3 -0.463 y^2 +0.0344 y +0.21 1
Affine cubic: f(x,y,z) = -0.158 x*z^2 -0.0655 y*z^2 +0.197 z^2 +0.0421 x^2*z -0.017 x*y*z -0.0187 x*z -0.188 y^2*z +0.174 y*z +0.164 z -0.611 x^3 -0.336 x^2*y -0.0692 x^2 -0.217 x*y^2 -0.0998 x*y -0.0153 x -0.169 y^3 -0.463 y^2 +0.0344 y +0.21 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].