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I'm looking for a name for my class that manipulates 4x4 matrices that handle position, rotation, and scale. Is there a common word that encompasses all three?

(I'm splitting the matrix math into its own file/class.)

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transform, or transformation

http://en.wikipedia.org/wiki/Transformation_matrix

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If you add shear to your list (although rarely used in games), it is generally known in mathematics as an affine transformation.

The general term 'transformation' has been mentioned already, is a usually considered a superset and includes projection transformations as well (which are not affine).

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I've seen PRS used (position, rotation, scale), but "transformation matrix" is a pretty informative name, and also covers other kinds of transformations (skewing etc).

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I've seen several engines shorten the term to Xform as well.

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Some variant of Transform or Transformation would work.

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