Random Gaussian cubic surface Seed: 148 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0306 x*z^2 -0.131 y*z^2 +0.379 z^2 +0.0906 x^2*z +0.023 x*y*z -0.199 x*z -0.299 y^2*z -0.448 y*z -0.169 z -0.055 x^3 -0.166 x^2*y +0.355 x^2 +0.355 x*y^2 -0.111 x*y +0.0433 x -0.18 y^3 -0.268 y^2 -0.00219 y -0.264 1
Affine cubic: f(x,y,z) = 0.0306 x*z^2 -0.131 y*z^2 +0.379 z^2 +0.0906 x^2*z +0.023 x*y*z -0.199 x*z -0.299 y^2*z -0.448 y*z -0.169 z -0.055 x^3 -0.166 x^2*y +0.355 x^2 +0.355 x*y^2 -0.111 x*y +0.0433 x -0.18 y^3 -0.268 y^2 -0.00219 y -0.264 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].