Random Gaussian cubic surface Seed: 47 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.147 x*z^2 +0.0214 y*z^2 -0.418 z^2 -0.427 x^2*z -0.31 x*y*z -0.176 x*z -0.162 y^2*z -0.101 y*z -0.042 z -0.193 x^3 +0.00101 x^2*y +0.13 x^2 +0.0599 x*y^2 +0.194 x*y +0.403 x -0.139 y^3 +0.353 y^2 -0.233 y -0.0137 1
Affine cubic: f(x,y,z) = -0.147 x*z^2 +0.0214 y*z^2 -0.418 z^2 -0.427 x^2*z -0.31 x*y*z -0.176 x*z -0.162 y^2*z -0.101 y*z -0.042 z -0.193 x^3 +0.00101 x^2*y +0.13 x^2 +0.0599 x*y^2 +0.194 x*y +0.403 x -0.139 y^3 +0.353 y^2 -0.233 y -0.0137 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].