Random Gaussian cubic surface Seed: 233 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.307 x*z^2 +0.282 y*z^2 +0.311 z^2 +0.302 x^2*z -0.0804 x*y*z +0.219 x*z -0.044 y^2*z -0.00183 y*z -0.442 z -0.281 x^3 +0.0161 x^2*y +0.184 x^2 +0.204 x*y^2 +0.261 x*y +0.11 x +0.0976 y^3 +0.27 y^2 +0.0368 y +0.26 1
Affine cubic: f(x,y,z) = 0.307 x*z^2 +0.282 y*z^2 +0.311 z^2 +0.302 x^2*z -0.0804 x*y*z +0.219 x*z -0.044 y^2*z -0.00183 y*z -0.442 z -0.281 x^3 +0.0161 x^2*y +0.184 x^2 +0.204 x*y^2 +0.261 x*y +0.11 x +0.0976 y^3 +0.27 y^2 +0.0368 y +0.26 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].