Random Gaussian cubic surface Seed: 260 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.132 x*z^2 +0.0693 y*z^2 +0.111 z^2 +0.554 x^2*z -0.0839 x*y*z +0.135 x*z -0.00599 y^2*z -0.0737 y*z +0.267 z -0.0471 x^3 -0.407 x^2*y +0.13 x^2 -0.3 x*y^2 -0.432 x*y -0.0684 x -0.0198 y^3 -0.217 y^2 +0.205 y -0.0334 1
Affine cubic: f(x,y,z) = -0.132 x*z^2 +0.0693 y*z^2 +0.111 z^2 +0.554 x^2*z -0.0839 x*y*z +0.135 x*z -0.00599 y^2*z -0.0737 y*z +0.267 z -0.0471 x^3 -0.407 x^2*y +0.13 x^2 -0.3 x*y^2 -0.432 x*y -0.0684 x -0.0198 y^3 -0.217 y^2 +0.205 y -0.0334 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].