The paper describes an algorithm derivation of rotation in the three-dimensional space, which is an efficient method for rotating objects in the space. The key in the derivation process is to summarize the many thoughts on this issue, included the geometric algebra, coordinate transformation, linear space and matrix operations, and analysis of some possible algorithm of rotation, such as basic rotation, the combination of rotations and coordinates system transformation. Finally, obtains a matrix as a formula for the free-rotation in the three dimensions.
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