Find nearest rotation for cube

I have c开发者_JAVA百科amera that look at cube from above. I can rotate cube so cube can have rotation values like z=258.18594 x=1. I need advice how to get nearest rotation with cube stand on ground and camera see top face.

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Look for Quaternion mathematics and Quaternion interpolation. This will make the task rather easy.

See also Nearest Neighbours using Quaternions