Plotting: lines that should be straight are curved

Question

When plotting a certain figure in Mathematica I noticed that some lines that should be straight ended up being curved in a certain periodic manner. I was hoping that somebody could help me fix this. A minimal working example of the code is provided below, with the resulting figure that Mathematica produces. I plot two parts of a hyperboloid $x^2+y^2-z^2=1$, namely the part with $y+z>0$ (green) and the part with $y+z<0$ (yellow). The lines where the two surfaces meet should be straight, but it has a certain periodic feature to it, which should not be there. Does anybody know how to fix this?

b = 5;
a = 10;

GreenPart = ContourPlot3D[
   -z^2 + x^2 + y^2 ==   1, {x, -a, a}, {y, -a, a}, {z, -a, a} , 
   RegionFunction -> 
    Function[{x, y, z}, y + z > 0  && z < b && z > -b], 
   ContourStyle -> RGBColor[0.0, 0.6, 0.1, 0.9],  Mesh -> None, 
   Axes -> False, Boxed -> False, AxesOrigin -> {0, 0, 0}
   ];
YellowPart = ContourPlot3D[
   -z^2 + x^2 + y^2 ==   1, {x, -a, a}, {y, -a, a} , {z, -a, a}, 
   RegionFunction -> 
    Function[{x, y, z}, (y + z < 0) && z < b && z > -b], 
   ContourStyle -> {RGBColor[1, 1, .0, .5]}, Mesh -> None, 
   Axes -> False, Boxed -> False, AxesOrigin -> {0, 0, 0}
   ];

Show[
 GreenPart, YellowPart,
 Graphics3D[
  {Red, Thickness[0.005], Arrowheads[0.03], 
   Arrow[{{0, 0, 0}, {b + 2, 0, 0}}], 
   Arrow[{{0, 0, 0}, {0, 0, b + 2}}], 
   Arrow[{{0, 0, 0}, {0, b + 2, 0}}]}
  ],
 Graphics3D[
  {Text[Style[x, 35, Italic, Bold, 
     FontFamily -> "Times New Roman"], {b + 3, 0, 0.2}], 
   Text[Style[y, 35, Italic, Bold, FontFamily -> "Times New Roman"],
     {0, b + 3, 0}], 
   Text[Style[z, 35, Italic, Bold, 
     FontFamily -> "Times New Roman"], {0, 0, b + 3.4}]}
  ],
 ImageSize -> Large,
 ViewPoint -> {2.5, 5, 1}
 ]

Answer 1

It looks like it's just due to the inner interpolation. Simply adding PlotPoints -> 50 to GreenPart and YellowPart does the job.