Random Gaussian cubic surface Seed: 482 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.12 x*z^2 +0.146 y*z^2 -0.0818 z^2 +0.299 x^2*z -0.0378 x*y*z -0.187 x*z -0.169 y^2*z +0.0216 y*z -0.125 z -0.284 x^3 -0.0105 x^2*y -0.0132 x^2 +0.162 x*y^2 +0.671 x*y -0.0441 x -0.347 y^3 -0.147 y^2 +0.108 y +0.274 1
Affine cubic: f(x,y,z) = 0.12 x*z^2 +0.146 y*z^2 -0.0818 z^2 +0.299 x^2*z -0.0378 x*y*z -0.187 x*z -0.169 y^2*z +0.0216 y*z -0.125 z -0.284 x^3 -0.0105 x^2*y -0.0132 x^2 +0.162 x*y^2 +0.671 x*y -0.0441 x -0.347 y^3 -0.147 y^2 +0.108 y +0.274 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].