# Calculate weighted mean point from array of 3D point.

I have a set of points whose positions are represented by 3D vectors. Each point has the associated weight in range from 0 to 1. The sum of all weights doesn't equal to 1.

How should the weighted mean point be calculated from the whole set of points?

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I don't understand "I have a set of points set by 3D vectors representing their positions." Do you mean something like "I have a set of points whose positions are represented by 3D vectors"? –  joriki Oct 31 '12 at 12:42
Yes, you're right. –  BartoNaz Oct 31 '12 at 12:42

The process is called normalization, and you simly divide each weight by the sum of all the weights: $$w_i \rightarrow \frac{w_i}{\sum w_i}$$ You can easily verify that the sum of the new weights is now $1$.
The mean vector is given by the sum: $${\bf{v}} = \sum w_i \bf{v}_i$$