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https://issues.apache.org/jira/browse/MATH-1284?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14973146#comment-14973146
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Luc Maisonobe commented on MATH-1284:
-------------------------------------

I agree that vector is not a point.
This issue was discussed (shortly) on the developers list on May 22nd 2011.
You can look here 
<http://mail-archives.apache.org/mod_mbox/commons-dev/201105.mbox/browser> for
the thread or here 
<http://commons.markmail.org/search/list:org.apache.common.dev+%22affine+and+vector+spaces%22>.

One argument for merging was that the difference was too subtle and merging the 
two concepts was quite common.
The other argument was that our interface is not restricted to Euclidean space 
but also encompasses spherical
geometry (we do use it for BSP trees on the 1-sphere and on the 2-sphere for 
example).

So we decided to stick to a single representation and in the Vector Javadoc we 
state:

 This interface represents a generic vector in a vectorial space or a point in 
an affine space.

This implies users are free to decide by themselves what is the semantic of the 
object they use.

The Transform interface defined in the lower partitioning package needs to know 
about the semantics.
Therefore, it specifically states it represents a transform in *affine* space. 
On the other hand, the
Rotation class in the euclidean.threed package is an operator acting in a 
vector space, and it does
*not* implement the aforementioned Transform interface.

I would indeed be glad to separate the two concepts, but has to think really a 
lot about it
in spherical geometry.

> Vector is-not-a Point
> ---------------------
>
>                 Key: MATH-1284
>                 URL: https://issues.apache.org/jira/browse/MATH-1284
>             Project: Commons Math
>          Issue Type: Bug
>    Affects Versions: 3.5
>            Reporter: Roman Werpachowski
>            Priority: Minor
>
> The class hierarchy for geometry claims that Vector is-a Point: 
> https://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math3/geometry/Point.html
> This is mathematically incorrect, see e.g. 
> http://math.stackexchange.com/a/645827
> Just because they share the same numerical representation, Point and Vector 
> shouldn't be crammed into a common class hierarchy.



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