Random Gaussian cubic surface Seed: 159 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.176 x*z^2 -0.308 y*z^2 +0.201 z^2 -0.0711 x^2*z +0.26 x*y*z +0.0315 x*z -0.133 y^2*z +0.0519 y*z +0.254 z -0.305 x^3 -0.0279 x^2*y -0.481 x^2 -0.115 x*y^2 -0.11 x*y -0.301 x +0.358 y^3 +0.323 y^2 -0.0218 y -0.0303 1
Affine cubic: f(x,y,z) = -0.176 x*z^2 -0.308 y*z^2 +0.201 z^2 -0.0711 x^2*z +0.26 x*y*z +0.0315 x*z -0.133 y^2*z +0.0519 y*z +0.254 z -0.305 x^3 -0.0279 x^2*y -0.481 x^2 -0.115 x*y^2 -0.11 x*y -0.301 x +0.358 y^3 +0.323 y^2 -0.0218 y -0.0303 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].