Random Gaussian cubic surface Seed: 208 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0534 x*z^2 -0.291 y*z^2 -0.266 z^2 +0.145 x^2*z -0.116 x*y*z -0.11 x*z +0.143 y^2*z -0.325 y*z +0.0444 z -0.12 x^3 +0.361 x^2*y +0.0723 x^2 -0.138 x*y^2 +0.475 x*y +0.255 x +0.254 y^3 -0.196 y^2 -0.153 y +0.285 1
Affine cubic: f(x,y,z) = -0.0534 x*z^2 -0.291 y*z^2 -0.266 z^2 +0.145 x^2*z -0.116 x*y*z -0.11 x*z +0.143 y^2*z -0.325 y*z +0.0444 z -0.12 x^3 +0.361 x^2*y +0.0723 x^2 -0.138 x*y^2 +0.475 x*y +0.255 x +0.254 y^3 -0.196 y^2 -0.153 y +0.285 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].