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I have two dataset with Cartesian data points. I would like to uniformly translate the coordinates of one dataset to be properly rotated and on top of the other (having a certain max and min for all the dimensions) but maintaining the integrity spacing of the elements in the moved data set. I know this is very simple, Can someone give me the formula? For instance

old set

1, 0.000 0.000 0.000

2, 1.458 0.000 0.000

...

9572, 16.646 -3.778 19.771

new dataset

1, 148.612 -24.810 67.566

2, 148.618 -25.469 68.866

...

9572, 130.160 -25.318 86.045

Thank you

Here is a link to what I want to do only with three dimensions. http://i47.tinypic.com/2gxofms.png

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    @BenMillwood my two datasets are a plot of a cup and something that fits in the cup...properly rotated means fitting in the cup2012-09-17

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Once you have decided on the parameters of your rotation, the matrix multiplication is given in Wikipedia's Rotation Matrix article under "In three dimensions". For the translation, just add the desired amount to each coordinate. Determining what translation and rotation is required is not simple. You might search under "image registration" for some ideas.

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    i drew a 2d picture of what i want to do and posted it to a link in the question. i understand your explanation but I still don't understand how to implement your suggested solution.2012-09-17