Random Gaussian cubic surface Seed: 264 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0189 x*z^2 +0.337 y*z^2 +0.453 z^2 -0.0765 x^2*z +0.14 x*y*z +0.0507 x*z -0.475 y^2*z -0.122 y*z -0.0835 z +0.297 x^3 +0.182 x^2*y -0.364 x^2 -0.0436 x*y^2 -0.0911 x*y +0.0931 x -0.274 y^3 -0.139 y^2 +0.097 y +0.171 1
Affine cubic: f(x,y,z) = 0.0189 x*z^2 +0.337 y*z^2 +0.453 z^2 -0.0765 x^2*z +0.14 x*y*z +0.0507 x*z -0.475 y^2*z -0.122 y*z -0.0835 z +0.297 x^3 +0.182 x^2*y -0.364 x^2 -0.0436 x*y^2 -0.0911 x*y +0.0931 x -0.274 y^3 -0.139 y^2 +0.097 y +0.171 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].