Combining Two 3D Rotations

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The concentric rotations and can be combined either by doing first and then , written as , or first and then , written as . This right-to-left notation comes from the algebra of dot products, and , where is a vector and and are the matrices representing the rotations and .

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In general, .

You can vary the axes of rotation by changing the spherical coordinates of their corresponding vectors.

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Contributed by: George Beck and Jeff Bryant (September 2007)
Open content licensed under CC BY-NC-SA


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