Random Gaussian cubic surface Seed: 429 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.153 x*z^2 +0.148 y*z^2 -0.384 z^2 +0.055 x^2*z +0.23 x*y*z -0.13 x*z -0.242 y^2*z -0.0247 y*z +0.119 z +0.205 x^3 +0.162 x^2*y -0.462 x^2 -0.0412 x*y^2 -0.265 x*y -0.159 x -0.0348 y^3 +0.0346 y^2 -0.0917 y +0.522 1
Affine cubic: f(x,y,z) = 0.153 x*z^2 +0.148 y*z^2 -0.384 z^2 +0.055 x^2*z +0.23 x*y*z -0.13 x*z -0.242 y^2*z -0.0247 y*z +0.119 z +0.205 x^3 +0.162 x^2*y -0.462 x^2 -0.0412 x*y^2 -0.265 x*y -0.159 x -0.0348 y^3 +0.0346 y^2 -0.0917 y +0.522 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].