Random Gaussian cubic surface Seed: 243 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.156 x*z^2 +0.00725 y*z^2 +0.182 z^2 -0.274 x^2*z +0.189 x*y*z +0.32 x*z +0.0974 y^2*z +0.0429 y*z -0.209 z +0.244 x^3 +0.0814 x^2*y -0.164 x^2 -0.377 x*y^2 +0.164 x*y -0.313 x -0.238 y^3 -0.251 y^2 -0.421 y +0.13 1
Affine cubic: f(x,y,z) = -0.156 x*z^2 +0.00725 y*z^2 +0.182 z^2 -0.274 x^2*z +0.189 x*y*z +0.32 x*z +0.0974 y^2*z +0.0429 y*z -0.209 z +0.244 x^3 +0.0814 x^2*y -0.164 x^2 -0.377 x*y^2 +0.164 x*y -0.313 x -0.238 y^3 -0.251 y^2 -0.421 y +0.13 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].