Random Gaussian cubic surface Seed: 439 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = -0.264 x*z^2 +0.159 y*z^2 +0.116 z^2 +0.283 x^2*z -0.0636 x*y*z -0.435 x*z +0.0876 y^2*z +0.0146 y*z -0.284 z +0.226 x^3 +0.116 x^2*y -0.432 x^2 +0.13 x*y^2 +0.292 x*y +0.134 x -0.205 y^3 +0.307 y^2 -0.115 y -0.092 1
Affine cubic: f(x,y,z) = -0.264 x*z^2 +0.159 y*z^2 +0.116 z^2 +0.283 x^2*z -0.0636 x*y*z -0.435 x*z +0.0876 y^2*z +0.0146 y*z -0.284 z +0.226 x^3 +0.116 x^2*y -0.432 x^2 +0.13 x*y^2 +0.292 x*y +0.134 x -0.205 y^3 +0.307 y^2 -0.115 y -0.092 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 15 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].