Random Gaussian cubic surface Seed: 410 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0787 x*z^2 -0.0198 y*z^2 +0.205 z^2 -0.367 x^2*z +0.153 x*y*z -0.299 x*z +0.259 y^2*z -0.242 y*z -0.106 z +0.0667 x^3 -0.231 x^2*y +0.237 x^2 +0.135 x*y^2 -0.33 x*y -0.476 x -0.273 y^3 +0.007 y^2 +0.158 y +0.0138 1
Affine cubic: f(x,y,z) = -0.0787 x*z^2 -0.0198 y*z^2 +0.205 z^2 -0.367 x^2*z +0.153 x*y*z -0.299 x*z +0.259 y^2*z -0.242 y*z -0.106 z +0.0667 x^3 -0.231 x^2*y +0.237 x^2 +0.135 x*y^2 -0.33 x*y -0.476 x -0.273 y^3 +0.007 y^2 +0.158 y +0.0138 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].