Random Gaussian cubic surface Seed: 223 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0212 x*z^2 -0.201 y*z^2 -0.248 z^2 -0.117 x^2*z +0.212 x*y*z +0.144 x*z +0.0467 y^2*z +0.0819 y*z +0.301 z -0.058 x^3 +0.0358 x^2*y -0.257 x^2 +0.518 x*y^2 -0.106 x*y -0.474 x -0.257 y^3 -0.208 y^2 +0.107 y +0.15 1
Affine cubic: f(x,y,z) = -0.0212 x*z^2 -0.201 y*z^2 -0.248 z^2 -0.117 x^2*z +0.212 x*y*z +0.144 x*z +0.0467 y^2*z +0.0819 y*z +0.301 z -0.058 x^3 +0.0358 x^2*y -0.257 x^2 +0.518 x*y^2 -0.106 x*y -0.474 x -0.257 y^3 -0.208 y^2 +0.107 y +0.15 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].