Random Gaussian cubic surface Seed: 499 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.307 x*z^2 +0.0975 y*z^2 +0.108 z^2 -0.462 x^2*z +0.236 x*y*z +0.358 x*z -0.153 y^2*z -0.0762 y*z +0.0437 z +0.0719 x^3 -0.163 x^2*y -0.531 x^2 -0.0508 x*y^2 +0.21 x*y -0.056 x +0.149 y^3 -0.233 y^2 +0.0941 y +0.0884 1
Affine cubic: f(x,y,z) = -0.307 x*z^2 +0.0975 y*z^2 +0.108 z^2 -0.462 x^2*z +0.236 x*y*z +0.358 x*z -0.153 y^2*z -0.0762 y*z +0.0437 z +0.0719 x^3 -0.163 x^2*y -0.531 x^2 -0.0508 x*y^2 +0.21 x*y -0.056 x +0.149 y^3 -0.233 y^2 +0.0941 y +0.0884 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].