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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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inception

30 May 2009

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Date/TimeThumbnailDimensionsUserComment
current14:35, 25 November 2012Thumbnail for version as of 14:35, 25 November 2012424 × 535 (25 KB)Hawky.diddizLossless optimization
13:44, 31 May 2009Thumbnail for version as of 13:44, 31 May 2009424 × 535 (34 KB)MathsPoetryConstruction lines and rotation angle are now apparent, in the hope to make it clearer
06:37, 31 May 2009Thumbnail for version as of 06:37, 31 May 2009424 × 535 (29 KB)MathsPoetrySimplified version, hopefully easier to understand (it's never straightforward to understand 3D schemas)
18:38, 30 May 2009Thumbnail for version as of 18:38, 30 May 2009819 × 1,158 (69 KB)MathsPoetry{{Information |Description={{en|1=This picture has been made to illustrate article "Rotation matrix" (section about axis-angle formula) It shows a rotation R of 60° around an axis u = (1/√11, 1/√11, 3/√11) The rotation plane (orthogonal to u) is

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