Random Gaussian cubic surface Seed: 8 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.355 x*z^2 -0.273 y*z^2 -0.278 z^2 -0.0719 x^2*z -0.473 x*y*z -0.0386 x*z -0.196 y^2*z +0.183 y*z +0.196 z +0.285 x^3 +0.157 x^2*y -0.0108 x^2 +0.176 x*y^2 +0.308 x*y -0.134 x +0.125 y^3 -0.00873 y^2 +0.294 y -0.171 1
Affine cubic: f(x,y,z) = -0.355 x*z^2 -0.273 y*z^2 -0.278 z^2 -0.0719 x^2*z -0.473 x*y*z -0.0386 x*z -0.196 y^2*z +0.183 y*z +0.196 z +0.285 x^3 +0.157 x^2*y -0.0108 x^2 +0.176 x*y^2 +0.308 x*y -0.134 x +0.125 y^3 -0.00873 y^2 +0.294 y -0.171 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].