Random Gaussian cubic surface Seed: 221 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.201 x*z^2 -0.0716 y*z^2 -0.209 z^2 -0.124 x^2*z +0.283 x*y*z +0.00819 x*z +0.0793 y^2*z +0.271 y*z -0.431 z +0.111 x^3 +0.0322 x^2*y +0.0543 x^2 -0.152 x*y^2 +0.198 x*y -0.45 x +0.122 y^3 -0.0976 y^2 +0.289 y -0.401 1
Affine cubic: f(x,y,z) = 0.201 x*z^2 -0.0716 y*z^2 -0.209 z^2 -0.124 x^2*z +0.283 x*y*z +0.00819 x*z +0.0793 y^2*z +0.271 y*z -0.431 z +0.111 x^3 +0.0322 x^2*y +0.0543 x^2 -0.152 x*y^2 +0.198 x*y -0.45 x +0.122 y^3 -0.0976 y^2 +0.289 y -0.401 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].