# Plotting: lines that should be straight are curved

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}
] ## 1 Answer

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