Random Gaussian cubic surface Seed: 276 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.143 x*z^2 -0.166 y*z^2 -0.15 z^2 +0.323 x^2*z -0.0445 x*y*z -0.16 x*z -0.107 y^2*z -0.278 y*z -0.376 z +0.0651 x^3 +0.119 x^2*y -0.363 x^2 +0.317 x*y^2 +0.236 x*y -0.452 x -0.0341 y^3 +0.0872 y^2 -0.102 y +0.194 1
Affine cubic: f(x,y,z) = -0.143 x*z^2 -0.166 y*z^2 -0.15 z^2 +0.323 x^2*z -0.0445 x*y*z -0.16 x*z -0.107 y^2*z -0.278 y*z -0.376 z +0.0651 x^3 +0.119 x^2*y -0.363 x^2 +0.317 x*y^2 +0.236 x*y -0.452 x -0.0341 y^3 +0.0872 y^2 -0.102 y +0.194 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].