Random Gaussian cubic surface Seed: 305 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.529 x*z^2 -0.28 y*z^2 +0.329 z^2 +0.0414 x^2*z +0.178 x*y*z -0.465 x*z -0.35 y^2*z +0.0232 y*z +0.331 z -0.0571 x^3 -0.0139 x^2*y +0.101 x^2 +0.0659 x*y^2 +0.0457 x*y +0.0283 x -0.0494 y^3 -0.102 y^2 -0.123 y +0.0383 1
Affine cubic: f(x,y,z) = 0.529 x*z^2 -0.28 y*z^2 +0.329 z^2 +0.0414 x^2*z +0.178 x*y*z -0.465 x*z -0.35 y^2*z +0.0232 y*z +0.331 z -0.0571 x^3 -0.0139 x^2*y +0.101 x^2 +0.0659 x*y^2 +0.0457 x*y +0.0283 x -0.0494 y^3 -0.102 y^2 -0.123 y +0.0383 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].