Random Gaussian cubic surface Seed: 89 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.146 x*z^2 -0.0779 y*z^2 +0.306 z^2 +0.0847 x^2*z +0.267 x*y*z +0.0957 x*z +0.147 y^2*z +0.0335 y*z +0.164 z -0.253 x^3 +0.305 x^2*y -0.327 x^2 +0.0449 x*y^2 +0.00428 x*y -0.171 x +0.0977 y^3 -0.6 y^2 -0.277 y -0.0287 1
Affine cubic: f(x,y,z) = -0.146 x*z^2 -0.0779 y*z^2 +0.306 z^2 +0.0847 x^2*z +0.267 x*y*z +0.0957 x*z +0.147 y^2*z +0.0335 y*z +0.164 z -0.253 x^3 +0.305 x^2*y -0.327 x^2 +0.0449 x*y^2 +0.00428 x*y -0.171 x +0.0977 y^3 -0.6 y^2 -0.277 y -0.0287 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].