Random Gaussian cubic surface Seed: 88 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.178 x*z^2 -0.131 y*z^2 -0.257 z^2 +0.107 x^2*z -0.0962 x*y*z +0.225 x*z +0.232 y^2*z -0.124 y*z +0.365 z -0.259 x^3 -0.366 x^2*y -0.231 x^2 -0.137 x*y^2 +0.154 x*y +0.474 x -0.133 y^3 +0.134 y^2 +0.145 y +0.18 1
Affine cubic: f(x,y,z) = -0.178 x*z^2 -0.131 y*z^2 -0.257 z^2 +0.107 x^2*z -0.0962 x*y*z +0.225 x*z +0.232 y^2*z -0.124 y*z +0.365 z -0.259 x^3 -0.366 x^2*y -0.231 x^2 -0.137 x*y^2 +0.154 x*y +0.474 x -0.133 y^3 +0.134 y^2 +0.145 y +0.18 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].