Random Gaussian cubic surface Seed: 133 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.232 x*z^2 +0.0161 y*z^2 -0.183 z^2 -0.204 x^2*z +0.242 x*y*z +0.131 x*z -0.162 y^2*z -0.315 y*z +0.182 z +0.187 x^3 +0.00376 x^2*y -0.0825 x^2 +0.194 x*y^2 +0.477 x*y +0.258 x -0.0028 y^3 +0.0695 y^2 -0.196 y -0.469 1
Affine cubic: f(x,y,z) = -0.232 x*z^2 +0.0161 y*z^2 -0.183 z^2 -0.204 x^2*z +0.242 x*y*z +0.131 x*z -0.162 y^2*z -0.315 y*z +0.182 z +0.187 x^3 +0.00376 x^2*y -0.0825 x^2 +0.194 x*y^2 +0.477 x*y +0.258 x -0.0028 y^3 +0.0695 y^2 -0.196 y -0.469 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].