Random Gaussian cubic surface Seed: 326 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.27 x*z^2 -0.0501 y*z^2 -0.365 z^2 -0.149 x^2*z -0.145 x*y*z -0.0929 x*z +0.237 y^2*z +0.152 y*z +0.357 z -0.173 x^3 +0.151 x^2*y -0.188 x^2 -0.199 x*y^2 -0.502 x*y -0.149 x +0.0785 y^3 -0.06 y^2 +0.00959 y -0.348 1
Affine cubic: f(x,y,z) = 0.27 x*z^2 -0.0501 y*z^2 -0.365 z^2 -0.149 x^2*z -0.145 x*y*z -0.0929 x*z +0.237 y^2*z +0.152 y*z +0.357 z -0.173 x^3 +0.151 x^2*y -0.188 x^2 -0.199 x*y^2 -0.502 x*y -0.149 x +0.0785 y^3 -0.06 y^2 +0.00959 y -0.348 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].