Random Gaussian cubic surface Seed: 289 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.219 x*z^2 +0.555 y*z^2 -0.0472 z^2 -0.172 x^2*z +0.0618 x*y*z -0.279 x*z -0.0805 y^2*z +0.124 y*z +0.062 z +0.14 x^3 +0.294 x^2*y +0.213 x^2 +0.116 x*y^2 +0.436 x*y -0.0645 x +0.0007 y^3 +0.0511 y^2 +0.165 y +0.339 1
Affine cubic: f(x,y,z) = 0.219 x*z^2 +0.555 y*z^2 -0.0472 z^2 -0.172 x^2*z +0.0618 x*y*z -0.279 x*z -0.0805 y^2*z +0.124 y*z +0.062 z +0.14 x^3 +0.294 x^2*y +0.213 x^2 +0.116 x*y^2 +0.436 x*y -0.0645 x +0.0007 y^3 +0.0511 y^2 +0.165 y +0.339 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].