Re: inpolygon in 3D

John D'Errico wrote:
In article <e1mttn$tnj$1@xxxxxxxxxxxxx>, Gabriele Bulian <ruga@.REMOVENOSSSSPAM.libero.it> wrote:

b wrote:
If it's convex polygon, then there is function "inhull" at file
exchange which can do what ever you are loking for.
Is there something for the case of a closed 3D solid (not necessarily convex) defined by a patch a for which, at each face, the outer normal is known?


My approach, where a tessellation exists, is to compute
barycentric coordinates for each point in each simplex.

Its easier than it seems, since it only takes a single
massive matrix multiply. You can be careful here and
block it as I do so the problem does not exceed the
available memory.

If the coordinates are all in the interval [0,1],
then a point is inside that simplex. Clearly this is
insensitive to convexity of the overall object. And
as a bonus, it even provides a simple way to allow a
tolerance. A second bonus is it works in n-dimensions.
The objects I've tended to work with were often not
convex, so these factors were all importance.

If all you have is a hull, it is still possible to
generate a tessellation, even if its not convex.

John

MMM...I'm keeping on reading your message, but:
1) I don't understand how do you form simplex
2) what do u mean with baricentric
3) why the final check is in the interval [0,1]
Regarding tessellation, I think that a closed 3D patch could be considered a tessellation...isn't it?

Sorry for double reply,
Gab
.

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