Random Gaussian cubic surface Seed: 409 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.141 x*z^2 -0.184 y*z^2 -0.0364 z^2 +0.288 x^2*z +0.2 x*y*z -0.2 x*z -0.316 y^2*z +0.196 y*z -0.285 z -0.311 x^3 -0.239 x^2*y -0.137 x^2 +0.0612 x*y^2 +0.269 x*y -0.129 x +0.382 y^3 -0.108 y^2 +0.346 y -0.14 1
Affine cubic: f(x,y,z) = -0.141 x*z^2 -0.184 y*z^2 -0.0364 z^2 +0.288 x^2*z +0.2 x*y*z -0.2 x*z -0.316 y^2*z +0.196 y*z -0.285 z -0.311 x^3 -0.239 x^2*y -0.137 x^2 +0.0612 x*y^2 +0.269 x*y -0.129 x +0.382 y^3 -0.108 y^2 +0.346 y -0.14 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].