Random Gaussian cubic surface Seed: 424 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.446 x*z^2 +0.0123 y*z^2 +0.0746 z^2 +0.205 x^2*z -0.0297 x*y*z +0.162 x*z +0.182 y^2*z -0.0136 y*z +0.0268 z +0.33 x^3 +0.241 x^2*y +0.492 x^2 -0.299 x*y^2 +0.15 x*y -0.076 x +0.261 y^3 -0.282 y^2 +0.0196 y -0.131 1
Affine cubic: f(x,y,z) = -0.446 x*z^2 +0.0123 y*z^2 +0.0746 z^2 +0.205 x^2*z -0.0297 x*y*z +0.162 x*z +0.182 y^2*z -0.0136 y*z +0.0268 z +0.33 x^3 +0.241 x^2*y +0.492 x^2 -0.299 x*y^2 +0.15 x*y -0.076 x +0.261 y^3 -0.282 y^2 +0.0196 y -0.131 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].