Random Gaussian cubic surface Seed: 204 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.205 x*z^2 +0.0363 y*z^2 +0.49 z^2 +0.239 x^2*z +0.0124 x*y*z -0.183 x*z -0.179 y^2*z +0.0726 y*z -0.421 z +0.0245 x^3 -0.286 x^2*y -0.189 x^2 -0.0882 x*y^2 +0.241 x*y +0.0996 x +0.379 y^3 +0.203 y^2 -0.167 y +0.0661 1
Affine cubic: f(x,y,z) = 0.205 x*z^2 +0.0363 y*z^2 +0.49 z^2 +0.239 x^2*z +0.0124 x*y*z -0.183 x*z -0.179 y^2*z +0.0726 y*z -0.421 z +0.0245 x^3 -0.286 x^2*y -0.189 x^2 -0.0882 x*y^2 +0.241 x*y +0.0996 x +0.379 y^3 +0.203 y^2 -0.167 y +0.0661 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].