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https://issues.apache.org/jira/browse/GEOMETRY-32?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16934868#comment-16934868
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Matt Juntunen commented on GEOMETRY-32:
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{quote}Really? This is actually a question: I don't know why it is a
requirement (nor where it is defined).
{quote}
I picture a region as a connected subset of the points in a space (see
[here|http://example.com/]). Therefore, the transformed region should be the
same as applying the transform to all of the points in that subset. I don't
have a formal proof of that statement, but I believe it holds nonetheless. The
flipping of the inside and outside of the regions we're talking about here is
simply a by-product of the fact that we're using oriented hyperplanes to test
points for inclusion in the region. For example, if we had a triangle in 2D and
defined our region using 3 points and barycentric coordinates instead of
oriented hyperplanes, then there would be no flipping of the inside and outside
of the region when transformed by a reflection. The same would be true if we
used unoriented line segments and winding numbers. The requirement to flip the
inside and outside of our oriented-hyperplane-bounded regions in certain
situations is just a requirement of how we're implementing the region inclusion
test, and not a property of the region itself.
> BSPTree Updates
> ---------------
>
> Key: GEOMETRY-32
> URL: https://issues.apache.org/jira/browse/GEOMETRY-32
> Project: Apache Commons Geometry
> Issue Type: Improvement
> Components: core
> Reporter: Matt Juntunen
> Priority: Major
> Labels: pull-request-available
> Time Spent: 20m
> Remaining Estimate: 0h
>
> The following updates should be made to the BSPTree class:
> - add an {{isLeaf()}} method to replace all of the {{node.getCut() == null}}
> expressions
> - add unit tests
> _Edit [2019-02-17]:_
> Additional goals:
> - Refactor the API to split the idea of a general BSPTree and a BSPTree used
> for defining in/out regions. This could result in a BSPTree interface and a
> RegionBSPTree interface. The goal here is to allow end-users to create their
> own extensions of these classes and specialize them for their own
> applications (for example, to implement spatial sorting or other algorithms).
> This will be one of the only planned extension points in the library.
> - Make the API easier to use and extend and reduce the necessity of casting
> (especially unchecked casting) as much as possible.
> - Add the idea of convex subhyperplanes to allow for more efficient tree
> construction.
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