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Rotating heightmap

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I have a heightmap that defines a surface in [0,1]^3. I want to rotate the surface about the x or z axis. However, when doing this, part of the surface will go outside [0,1]^3 and some "empty space" will be rotated in; this is OK, but I am wondering what the best way to reconstruct the rotated heightmap would be. Right now I am thinking: 1. From heightmap, rebuild (x,y,z) at each grid point. 2. Do Rotation 3. Rebuild heightmap from rotated grid points. Just wondering if there is a more efficient way I am missing.

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