Random Gaussian cubic surface Seed: 407 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.133 x*z^2 -0.0212 y*z^2 +0.284 z^2 -0.275 x^2*z +0.246 x*y*z -0.0424 x*z +0.108 y^2*z +0.17 y*z -0.11 z +0.0776 x^3 -0.409 x^2*y +0.259 x^2 +0.212 x*y^2 -0.389 x*y +0.48 x +0.114 y^3 -0.151 y^2 -0.0211 y -0.0885 1
Affine cubic: f(x,y,z) = 0.133 x*z^2 -0.0212 y*z^2 +0.284 z^2 -0.275 x^2*z +0.246 x*y*z -0.0424 x*z +0.108 y^2*z +0.17 y*z -0.11 z +0.0776 x^3 -0.409 x^2*y +0.259 x^2 +0.212 x*y^2 -0.389 x*y +0.48 x +0.114 y^3 -0.151 y^2 -0.0211 y -0.0885 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].