Random Gaussian cubic surface Seed: 121 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0518 x*z^2 -0.122 y*z^2 +0.0551 z^2 -0.228 x^2*z +0.311 x*y*z +0.125 x*z +0.205 y^2*z -0.0543 y*z +0.502 z -0.0784 x^3 -0.124 x^2*y +0.166 x^2 -0.335 x*y^2 -0.184 x*y +0.146 x -0.2 y^3 -0.472 y^2 -0.02 y +0.194 1
Affine cubic: f(x,y,z) = -0.0518 x*z^2 -0.122 y*z^2 +0.0551 z^2 -0.228 x^2*z +0.311 x*y*z +0.125 x*z +0.205 y^2*z -0.0543 y*z +0.502 z -0.0784 x^3 -0.124 x^2*y +0.166 x^2 -0.335 x*y^2 -0.184 x*y +0.146 x -0.2 y^3 -0.472 y^2 -0.02 y +0.194 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].