Random Gaussian cubic surface Seed: 447 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0267 x*z^2 -0.217 y*z^2 +0.0642 z^2 +0.14 x^2*z -0.0151 x*y*z -0.144 x*z +0.0372 y^2*z -0.32 y*z +0.407 z -0.21 x^3 +0.433 x^2*y -0.399 x^2 -0.168 x*y^2 +0.0737 x*y -0.162 x +0.0219 y^3 +0.0364 y^2 +0.424 y -0.072 1
Affine cubic: f(x,y,z) = 0.0267 x*z^2 -0.217 y*z^2 +0.0642 z^2 +0.14 x^2*z -0.0151 x*y*z -0.144 x*z +0.0372 y^2*z -0.32 y*z +0.407 z -0.21 x^3 +0.433 x^2*y -0.399 x^2 -0.168 x*y^2 +0.0737 x*y -0.162 x +0.0219 y^3 +0.0364 y^2 +0.424 y -0.072 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].