Random Gaussian cubic surface Seed: 217 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.259 x*z^2 -0.152 y*z^2 -0.318 z^2 +0.029 x^2*z +0.365 x*y*z +0.0944 x*z -0.0875 y^2*z +0.207 y*z -0.0575 z -0.00949 x^3 -0.199 x^2*y +0.389 x^2 -0.35 x*y^2 +0.405 x*y -0.0699 x -0.3 y^3 +0.0763 y^2 -0.135 y +0.122 1
Affine cubic: f(x,y,z) = -0.259 x*z^2 -0.152 y*z^2 -0.318 z^2 +0.029 x^2*z +0.365 x*y*z +0.0944 x*z -0.0875 y^2*z +0.207 y*z -0.0575 z -0.00949 x^3 -0.199 x^2*y +0.389 x^2 -0.35 x*y^2 +0.405 x*y -0.0699 x -0.3 y^3 +0.0763 y^2 -0.135 y +0.122 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].