Random Gaussian cubic surface Seed: 256 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.109 x*z^2 -0.201 y*z^2 +0.407 z^2 -0.107 x^2*z -0.053 x*y*z -0.242 x*z +0.276 y^2*z +0.345 y*z +0.214 z +0.049 x^3 +0.271 x^2*y -0.0218 x^2 +0.203 x*y^2 +0.136 x*y -0.196 x -0.095 y^3 -0.428 y^2 -0.0126 y +0.319 1
Affine cubic: f(x,y,z) = 0.109 x*z^2 -0.201 y*z^2 +0.407 z^2 -0.107 x^2*z -0.053 x*y*z -0.242 x*z +0.276 y^2*z +0.345 y*z +0.214 z +0.049 x^3 +0.271 x^2*y -0.0218 x^2 +0.203 x*y^2 +0.136 x*y -0.196 x -0.095 y^3 -0.428 y^2 -0.0126 y +0.319 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].