Random Gaussian cubic surface Seed: 72 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.245 x*z^2 -0.00692 y*z^2 +0.143 z^2 -0.412 x^2*z -0.341 x*y*z -0.234 x*z +0.245 y^2*z +0.272 y*z +0.0784 z +0.11 x^3 -0.148 x^2*y -0.287 x^2 +0.116 x*y^2 +0.184 x*y -0.0216 x -0.483 y^3 +0.0633 y^2 +0.0301 y -0.187 1
Affine cubic: f(x,y,z) = -0.245 x*z^2 -0.00692 y*z^2 +0.143 z^2 -0.412 x^2*z -0.341 x*y*z -0.234 x*z +0.245 y^2*z +0.272 y*z +0.0784 z +0.11 x^3 -0.148 x^2*y -0.287 x^2 +0.116 x*y^2 +0.184 x*y -0.0216 x -0.483 y^3 +0.0633 y^2 +0.0301 y -0.187 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].