Random Gaussian cubic surface Seed: 491 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0154 x*z^2 +0.13 y*z^2 +0.144 z^2 +0.352 x^2*z -0.319 x*y*z -0.142 x*z -0.151 y^2*z -0.34 y*z +0.331 z -0.201 x^3 -0.113 x^2*y +0.127 x^2 +0.158 x*y^2 +0.305 x*y +0.129 x +0.358 y^3 +0.0748 y^2 -0.321 y -0.17 1
Affine cubic: f(x,y,z) = 0.0154 x*z^2 +0.13 y*z^2 +0.144 z^2 +0.352 x^2*z -0.319 x*y*z -0.142 x*z -0.151 y^2*z -0.34 y*z +0.331 z -0.201 x^3 -0.113 x^2*y +0.127 x^2 +0.158 x*y^2 +0.305 x*y +0.129 x +0.358 y^3 +0.0748 y^2 -0.321 y -0.17 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].