Random Gaussian cubic surface Seed: 58 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.176 x*z^2 +0.0282 y*z^2 -0.646 z^2 -0.428 x^2*z -0.232 x*y*z -0.068 x*z +0.226 y^2*z +0.0344 y*z -0.131 z -0.0972 x^3 -0.0666 x^2*y -0.0955 x^2 -0.243 x*y^2 -0.224 x*y -0.0196 x -0.0858 y^3 -0.301 y^2 +0.0506 y +0.0852 1
Affine cubic: f(x,y,z) = -0.176 x*z^2 +0.0282 y*z^2 -0.646 z^2 -0.428 x^2*z -0.232 x*y*z -0.068 x*z +0.226 y^2*z +0.0344 y*z -0.131 z -0.0972 x^3 -0.0666 x^2*y -0.0955 x^2 -0.243 x*y^2 -0.224 x*y -0.0196 x -0.0858 y^3 -0.301 y^2 +0.0506 y +0.0852 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].