Random Gaussian cubic surface Seed: 449 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0136 x*z^2 +0.109 y*z^2 +0.442 z^2 +0.195 x^2*z -0.103 x*y*z +0.00879 x*z -0.347 y^2*z -0.12 y*z +0.261 z +0.26 x^3 -0.177 x^2*y +0.22 x^2 -0.0334 x*y^2 -0.184 x*y -0.446 x -0.298 y^3 +0.0194 y^2 +0.139 y -0.225 1
Affine cubic: f(x,y,z) = 0.0136 x*z^2 +0.109 y*z^2 +0.442 z^2 +0.195 x^2*z -0.103 x*y*z +0.00879 x*z -0.347 y^2*z -0.12 y*z +0.261 z +0.26 x^3 -0.177 x^2*y +0.22 x^2 -0.0334 x*y^2 -0.184 x*y -0.446 x -0.298 y^3 +0.0194 y^2 +0.139 y -0.225 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].