Random Gaussian cubic surface Seed: 490 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.1 x*z^2 -0.255 y*z^2 -0.0276 z^2 -0.107 x^2*z +0.11 x*y*z +0.12 x*z -0.0159 y^2*z +0.114 y*z -0.0871 z +0.405 x^3 +0.227 x^2*y +0.00129 x^2 -0.623 x*y^2 -0.0129 x*y +0.0693 x -0.0188 y^3 +0.289 y^2 -0.291 y +0.298 1
Affine cubic: f(x,y,z) = -0.1 x*z^2 -0.255 y*z^2 -0.0276 z^2 -0.107 x^2*z +0.11 x*y*z +0.12 x*z -0.0159 y^2*z +0.114 y*z -0.0871 z +0.405 x^3 +0.227 x^2*y +0.00129 x^2 -0.623 x*y^2 -0.0129 x*y +0.0693 x -0.0188 y^3 +0.289 y^2 -0.291 y +0.298 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].