Random Gaussian cubic surface Seed: 229 (Gaussian coefficient and line-tracking seed)
Cubic: f(x,y,z) = 0.0193 x*z^2 +0.15 y*z^2 +0.0245 z^2 +0.0799 x^2*z +0.111 x*y*z +0.427 x*z -0.183 y^2*z +0.062 y*z +0.12 z -0.382 x^3 +0.053 x^2*y -0.177 x^2 +0.317 x*y^2 +0.0552 x*y +0.0153 x +0.0604 y^3 +0.57 y^2 -0.284 y +0.172 1
Affine cubic: f(x,y,z) = 0.0193 x*z^2 +0.15 y*z^2 +0.0245 z^2 +0.0799 x^2*z +0.111 x*y*z +0.427 x*z -0.183 y^2*z +0.062 y*z +0.12 z -0.382 x^3 +0.053 x^2*y -0.177 x^2 +0.317 x*y^2 +0.0552 x*y +0.0153 x +0.0604 y^3 +0.57 y^2 -0.284 y +0.172 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 3 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].