Random Gaussian cubic surface Seed: 240 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0957 x*z^2 -0.0345 y*z^2 +0.268 z^2 -0.145 x^2*z -0.0446 x*y*z -0.171 x*z +0.546 y^2*z -0.296 y*z +0.261 z -0.41 x^3 +0.156 x^2*y -0.274 x^2 +0.111 x*y^2 -0.151 x*y +0.315 x +0.037 y^3 +0.0616 y^2 +0.0603 y -0.0132 1
Affine cubic: f(x,y,z) = 0.0957 x*z^2 -0.0345 y*z^2 +0.268 z^2 -0.145 x^2*z -0.0446 x*y*z -0.171 x*z +0.546 y^2*z -0.296 y*z +0.261 z -0.41 x^3 +0.156 x^2*y -0.274 x^2 +0.111 x*y^2 -0.151 x*y +0.315 x +0.037 y^3 +0.0616 y^2 +0.0603 y -0.0132 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].