Random Gaussian cubic surface Seed: 226 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.179 x*z^2 +0.351 y*z^2 -0.336 z^2 -0.194 x^2*z -0.186 x*y*z +0.423 x*z -0.166 y^2*z +0.126 y*z +0.106 z -0.144 x^3 +0.102 x^2*y -0.266 x^2 +0.228 x*y^2 +0.334 x*y +0.247 x -0.00118 y^3 +0.00471 y^2 +0.0764 y +0.306 1
Affine cubic: f(x,y,z) = 0.179 x*z^2 +0.351 y*z^2 -0.336 z^2 -0.194 x^2*z -0.186 x*y*z +0.423 x*z -0.166 y^2*z +0.126 y*z +0.106 z -0.144 x^3 +0.102 x^2*y -0.266 x^2 +0.228 x*y^2 +0.334 x*y +0.247 x -0.00118 y^3 +0.00471 y^2 +0.0764 y +0.306 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].