Random Gaussian cubic surface Seed: 10 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.325 x*z^2 -0.214 y*z^2 -0.23 z^2 +0.0787 x^2*z -0.0732 x*y*z +0.0373 x*z +0.248 y^2*z +0.253 y*z +0.14 z -0.133 x^3 -0.222 x^2*y -0.24 x^2 -0.101 x*y^2 -0.0151 x*y -0.286 x -0.334 y^3 +0.0901 y^2 -0.546 y -0.0522 1
Affine cubic: f(x,y,z) = -0.325 x*z^2 -0.214 y*z^2 -0.23 z^2 +0.0787 x^2*z -0.0732 x*y*z +0.0373 x*z +0.248 y^2*z +0.253 y*z +0.14 z -0.133 x^3 -0.222 x^2*y -0.24 x^2 -0.101 x*y^2 -0.0151 x*y -0.286 x -0.334 y^3 +0.0901 y^2 -0.546 y -0.0522 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].