Random Gaussian cubic surface Seed: 470 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.255 x*z^2 -0.253 y*z^2 +0.14 z^2 -0.105 x^2*z +0.426 x*y*z +0.318 x*z -0.134 y^2*z -0.326 y*z +0.151 z +0.0547 x^3 +0.0342 x^2*y +0.0632 x^2 +0.457 x*y^2 -0.11 x*y -0.192 x +0.121 y^3 -0.116 y^2 -0.314 y -0.134 1
Affine cubic: f(x,y,z) = 0.255 x*z^2 -0.253 y*z^2 +0.14 z^2 -0.105 x^2*z +0.426 x*y*z +0.318 x*z -0.134 y^2*z -0.326 y*z +0.151 z +0.0547 x^3 +0.0342 x^2*y +0.0632 x^2 +0.457 x*y^2 -0.11 x*y -0.192 x +0.121 y^3 -0.116 y^2 -0.314 y -0.134 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 15 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].