Random Gaussian cubic surface Seed: 398 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.297 x*z^2 -0.276 y*z^2 -0.426 z^2 +0.226 x^2*z +0.0309 x*y*z -0.259 x*z -0.456 y^2*z -0.106 y*z -0.189 z +0.17 x^3 -0.104 x^2*y -0.156 x^2 -0.184 x*y^2 +0.0693 x*y +0.333 x -0.023 y^3 +0.0726 y^2 +0.00555 y -0.246 1
Affine cubic: f(x,y,z) = -0.297 x*z^2 -0.276 y*z^2 -0.426 z^2 +0.226 x^2*z +0.0309 x*y*z -0.259 x*z -0.456 y^2*z -0.106 y*z -0.189 z +0.17 x^3 -0.104 x^2*y -0.156 x^2 -0.184 x*y^2 +0.0693 x*y +0.333 x -0.023 y^3 +0.0726 y^2 +0.00555 y -0.246 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].