Random Gaussian cubic surface Seed: 471 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0697 x*z^2 +0.0278 y*z^2 +0.0098 z^2 +0.0954 x^2*z +0.102 x*y*z -0.157 x*z +0.0989 y^2*z +0.401 y*z +0.101 z -0.3 x^3 -0.101 x^2*y +0.074 x^2 -0.153 x*y^2 +0.477 x*y +0.0496 x -0.376 y^3 +0.296 y^2 +0.393 y +0.165 1
Affine cubic: f(x,y,z) = 0.0697 x*z^2 +0.0278 y*z^2 +0.0098 z^2 +0.0954 x^2*z +0.102 x*y*z -0.157 x*z +0.0989 y^2*z +0.401 y*z +0.101 z -0.3 x^3 -0.101 x^2*y +0.074 x^2 -0.153 x*y^2 +0.477 x*y +0.0496 x -0.376 y^3 +0.296 y^2 +0.393 y +0.165 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].