Random Gaussian cubic surface Seed: 479 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0185 x*z^2 -0.188 y*z^2 -0.185 z^2 -0.285 x^2*z -0.0573 x*y*z +0.259 x*z +0.0326 y^2*z +0.006 y*z -0.0558 z +0.381 x^3 +0.121 x^2*y -0.588 x^2 -0.128 x*y^2 +0.264 x*y -0.362 x -0.00664 y^3 +0.152 y^2 +0.0889 y +0.14 1
Affine cubic: f(x,y,z) = 0.0185 x*z^2 -0.188 y*z^2 -0.185 z^2 -0.285 x^2*z -0.0573 x*y*z +0.259 x*z +0.0326 y^2*z +0.006 y*z -0.0558 z +0.381 x^3 +0.121 x^2*y -0.588 x^2 -0.128 x*y^2 +0.264 x*y -0.362 x -0.00664 y^3 +0.152 y^2 +0.0889 y +0.14 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 15 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].