Random Gaussian cubic surface Seed: 45 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.163 x*z^2 -0.222 y*z^2 +0.0483 z^2 +0.301 x^2*z -0.053 x*y*z +0.0937 x*z +0.19 y^2*z +0.246 y*z -0.318 z +0.167 x^3 -0.00635 x^2*y -0.215 x^2 -0.242 x*y^2 -0.0811 x*y -0.355 x -0.521 y^3 +0.0228 y^2 +0.277 y -0.0861 1
Affine cubic: f(x,y,z) = -0.163 x*z^2 -0.222 y*z^2 +0.0483 z^2 +0.301 x^2*z -0.053 x*y*z +0.0937 x*z +0.19 y^2*z +0.246 y*z -0.318 z +0.167 x^3 -0.00635 x^2*y -0.215 x^2 -0.242 x*y^2 -0.0811 x*y -0.355 x -0.521 y^3 +0.0228 y^2 +0.277 y -0.0861 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 7 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].