Random Gaussian cubic surface Seed: 123 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.274 x*z^2 -0.102 y*z^2 +0.357 z^2 +0.0538 x^2*z +0.255 x*y*z +0.16 x*z -0.177 y^2*z +0.15 y*z -0.0878 z -0.0894 x^3 +0.0269 x^2*y -0.423 x^2 +0.331 x*y^2 -0.186 x*y +0.277 x +0.0378 y^3 +0.425 y^2 -0.183 y -0.0865 1
Affine cubic: f(x,y,z) = -0.274 x*z^2 -0.102 y*z^2 +0.357 z^2 +0.0538 x^2*z +0.255 x*y*z +0.16 x*z -0.177 y^2*z +0.15 y*z -0.0878 z -0.0894 x^3 +0.0269 x^2*y -0.423 x^2 +0.331 x*y^2 -0.186 x*y +0.277 x +0.0378 y^3 +0.425 y^2 -0.183 y -0.0865 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 15 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].