Random Gaussian cubic surface Seed: 352 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.17 x*z^2 -0.269 y*z^2 +0.081 z^2 -0.152 x^2*z -0.485 x*y*z -0.0118 x*z -0.193 y^2*z +0.0793 y*z -0.345 z -0.35 x^3 +0.254 x^2*y +0.132 x^2 +0.147 x*y^2 +0.0896 x*y -0.24 x -0.12 y^3 +0.236 y^2 +0.107 y +0.312 1
Affine cubic: f(x,y,z) = -0.17 x*z^2 -0.269 y*z^2 +0.081 z^2 -0.152 x^2*z -0.485 x*y*z -0.0118 x*z -0.193 y^2*z +0.0793 y*z -0.345 z -0.35 x^3 +0.254 x^2*y +0.132 x^2 +0.147 x*y^2 +0.0896 x*y -0.24 x -0.12 y^3 +0.236 y^2 +0.107 y +0.312 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].