Random Gaussian cubic surface Seed: 267 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0645 x*z^2 -0.036 y*z^2 +0.353 z^2 +0.0501 x^2*z +0.0872 x*y*z -0.0386 x*z -0.157 y^2*z -0.134 y*z -0.0917 z -0.0982 x^3 -0.216 x^2*y -0.372 x^2 +0.219 x*y^2 -0.121 x*y -0.607 x -0.0621 y^3 +0.268 y^2 +0.193 y +0.262 1
Affine cubic: f(x,y,z) = 0.0645 x*z^2 -0.036 y*z^2 +0.353 z^2 +0.0501 x^2*z +0.0872 x*y*z -0.0386 x*z -0.157 y^2*z -0.134 y*z -0.0917 z -0.0982 x^3 -0.216 x^2*y -0.372 x^2 +0.219 x*y^2 -0.121 x*y -0.607 x -0.0621 y^3 +0.268 y^2 +0.193 y +0.262 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].