Random Gaussian cubic surface Seed: 314 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.202 x*z^2 -0.181 y*z^2 +0.0121 z^2 +0.323 x^2*z +0.00971 x*y*z +0.113 x*z +0.043 y^2*z +0.0492 y*z -0.0483 z -0.0203 x^3 -0.595 x^2*y -0.17 x^2 +0.156 x*y^2 +0.398 x*y +0.294 x -0.0795 y^3 +0.0724 y^2 +0.37 y -0.0156 1
Affine cubic: f(x,y,z) = -0.202 x*z^2 -0.181 y*z^2 +0.0121 z^2 +0.323 x^2*z +0.00971 x*y*z +0.113 x*z +0.043 y^2*z +0.0492 y*z -0.0483 z -0.0203 x^3 -0.595 x^2*y -0.17 x^2 +0.156 x*y^2 +0.398 x*y +0.294 x -0.0795 y^3 +0.0724 y^2 +0.37 y -0.0156 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].