Random Gaussian cubic surface Seed: 389 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.039 x*z^2 -0.14 y*z^2 +0.116 z^2 -0.174 x^2*z +0.312 x*y*z +0.282 x*z +0.0446 y^2*z +0.047 y*z +0.242 z -0.0902 x^3 -0.128 x^2*y -0.512 x^2 -0.238 x*y^2 +0.289 x*y -0.167 x +0.0823 y^3 +0.34 y^2 -0.212 y -0.271 1
Affine cubic: f(x,y,z) = 0.039 x*z^2 -0.14 y*z^2 +0.116 z^2 -0.174 x^2*z +0.312 x*y*z +0.282 x*z +0.0446 y^2*z +0.047 y*z +0.242 z -0.0902 x^3 -0.128 x^2*y -0.512 x^2 -0.238 x*y^2 +0.289 x*y -0.167 x +0.0823 y^3 +0.34 y^2 -0.212 y -0.271 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].