Random Gaussian cubic surface Seed: 261 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.258 x*z^2 +0.293 y*z^2 +0.0272 z^2 -0.122 x^2*z +0.0174 x*y*z +0.0288 x*z +0.597 y^2*z -0.163 y*z -0.437 z +0.0367 x^3 +0.299 x^2*y -0.143 x^2 -0.0381 x*y^2 +0.135 x*y -0.0361 x +0.145 y^3 -0.0386 y^2 -0.149 y -0.282 1
Affine cubic: f(x,y,z) = -0.258 x*z^2 +0.293 y*z^2 +0.0272 z^2 -0.122 x^2*z +0.0174 x*y*z +0.0288 x*z +0.597 y^2*z -0.163 y*z -0.437 z +0.0367 x^3 +0.299 x^2*y -0.143 x^2 -0.0381 x*y^2 +0.135 x*y -0.0361 x +0.145 y^3 -0.0386 y^2 -0.149 y -0.282 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].