Random Gaussian cubic surface Seed: 251 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0924 x*z^2 +0.058 y*z^2 +0.375 z^2 -0.427 x^2*z +0.204 x*y*z +0.00174 x*z -0.251 y^2*z +0.0519 y*z -0.194 z -0.0482 x^3 -0.678 x^2*y +0.161 x^2 -0.0694 x*y^2 -0.049 x*y -0.101 x -0.015 y^3 -0.0413 y^2 -0.0172 y +0.112 1
Affine cubic: f(x,y,z) = -0.0924 x*z^2 +0.058 y*z^2 +0.375 z^2 -0.427 x^2*z +0.204 x*y*z +0.00174 x*z -0.251 y^2*z +0.0519 y*z -0.194 z -0.0482 x^3 -0.678 x^2*y +0.161 x^2 -0.0694 x*y^2 -0.049 x*y -0.101 x -0.015 y^3 -0.0413 y^2 -0.0172 y +0.112 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].