Random Gaussian cubic surface Seed: 17 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.221 x*z^2 +0.0681 y*z^2 -0.109 z^2 -0.253 x^2*z -0.381 x*y*z +0.00375 x*z -0.163 y^2*z -0.175 y*z -0.0446 z -0.0104 x^3 -0.458 x^2*y +0.186 x^2 -0.408 x*y^2 +0.374 x*y +0.119 x -0.0949 y^3 +0.27 y^2 +0.00418 y +0.139 1
Affine cubic: f(x,y,z) = 0.221 x*z^2 +0.0681 y*z^2 -0.109 z^2 -0.253 x^2*z -0.381 x*y*z +0.00375 x*z -0.163 y^2*z -0.175 y*z -0.0446 z -0.0104 x^3 -0.458 x^2*y +0.186 x^2 -0.408 x*y^2 +0.374 x*y +0.119 x -0.0949 y^3 +0.27 y^2 +0.00418 y +0.139 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].