Random Gaussian cubic surface Seed: 365 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.0368 x*z^2 +0.0254 y*z^2 -0.017 z^2 +0.285 x^2*z -0.185 x*y*z -0.138 x*z -0.216 y^2*z +0.197 y*z +0.0238 z -0.572 x^3 +0.177 x^2*y -0.13 x^2 -0.149 x*y^2 -0.158 x*y -0.265 x +0.304 y^3 -0.354 y^2 -0.0127 y +0.258 1
Affine cubic: f(x,y,z) = -0.0368 x*z^2 +0.0254 y*z^2 -0.017 z^2 +0.285 x^2*z -0.185 x*y*z -0.138 x*z -0.216 y^2*z +0.197 y*z +0.0238 z -0.572 x^3 +0.177 x^2*y -0.13 x^2 -0.149 x*y^2 -0.158 x*y -0.265 x +0.304 y^3 -0.354 y^2 -0.0127 y +0.258 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].