Random Gaussian cubic surface Seed: 181 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.132 x*z^2 -0.275 y*z^2 -0.288 z^2 -0.45 x^2*z -0.0353 x*y*z +0.186 x*z -0.0425 y^2*z +0.393 y*z -0.115 z +0.277 x^3 -0.0571 x^2*y -0.287 x^2 +0.156 x*y^2 -0.0538 x*y +0.3 x -0.099 y^3 +0.0636 y^2 +0.0698 y -0.342 1
Affine cubic: f(x,y,z) = -0.132 x*z^2 -0.275 y*z^2 -0.288 z^2 -0.45 x^2*z -0.0353 x*y*z +0.186 x*z -0.0425 y^2*z +0.393 y*z -0.115 z +0.277 x^3 -0.0571 x^2*y -0.287 x^2 +0.156 x*y^2 -0.0538 x*y +0.3 x -0.099 y^3 +0.0636 y^2 +0.0698 y -0.342 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].