Random Gaussian cubic surface Seed: 206 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.162 x*z^2 -0.0215 y*z^2 +0.324 z^2 +0.12 x^2*z -0.0479 x*y*z -0.102 x*z -0.272 y^2*z -0.424 y*z -0.0107 z +0.285 x^3 -0.125 x^2*y -0.213 x^2 -0.0883 x*y^2 +0.134 x*y +0.184 x +0.558 y^3 -0.126 y^2 +0.223 y +0.0923 1
Affine cubic: f(x,y,z) = 0.162 x*z^2 -0.0215 y*z^2 +0.324 z^2 +0.12 x^2*z -0.0479 x*y*z -0.102 x*z -0.272 y^2*z -0.424 y*z -0.0107 z +0.285 x^3 -0.125 x^2*y -0.213 x^2 -0.0883 x*y^2 +0.134 x*y +0.184 x +0.558 y^3 -0.126 y^2 +0.223 y +0.0923 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].