File:Rotation decomposition.png

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Rotation_decomposition.png (424 × 535 pixels, file size: 25 KB, MIME type: image/png)

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Summary

Description
English: This picture has been made to illustrate article "Rotation matrix" (section about axis-angle formula)

It shows a rotation R of an angle θ = 60° around an axis u = (1/√11, 1/√11, 3/√11)

A vector v = (1/√3, 1/√3, 1/√3) is rotated to R(v)

  • v’s projection to u’s axis is P(v)
  • v’s projection to the orthogonal plane is (I − P)(v)
  • Q(v) is orthogonal to the other two
R = P + (I − P) cosθ + Q sinθ : that's the decomposition of R
Date
Source Own work
Author MathsPoetry
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30 May 2009

data size

25,831 byte

height

535 pixel

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424 pixel

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3a635fe85e597d3392ce40be729c81b1ac87429c

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Date/TimeThumbnailDimensionsUserComment
current15:35, 25 November 2012Thumbnail for version as of 15:35, 25 November 2012424 × 535 (25 KB)wikimediacommons>Hawky.diddizLossless optimization

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