# topology of geometries in gis

http://imm.io/2cpJ

What is the thinking of OGC to keep this point that "point have no boundry , it just has interior"... what do they mean?

this notation: `F**F*****`...still i am confused due to OGC model.

It should be `TFTTFTTFT` as far as I know: the point have no interior, it has just a boundary, so it should be an F and T relation between point and line.

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Could you supply a link to the OGC document you are quoting? – whuber Nov 24 '10 at 2:21
i have a pdf file.. can you tell me what it does mean F**F*****.. i ma finding intersection of point to line... – tina Nov 24 '10 at 2:24
i am applying 9-intersection modeling for 2d operations using c++ – tina Nov 24 '10 at 2:33
@Whuber how can i send you that pdf file ... – tina Nov 24 '10 at 2:53
You could upload it to google docs and post the share link. – Nathan W Nov 24 '10 at 3:46

I would have commented rather than answered, because there are already several good answers, but I don't have enough reputation yet to comment!

Caveat: I have to think hard when working with the DE-9IM and may have misunderstood your question, or the documents that I looked at.

You said you're testing the intersection of a point and a line. This answer, `F**F*****`, looks like the intersection of a line with a point. A "*" means that the answer doesn't matter, which would include each test of the point's "boundary" or "exterior", because a point only has an interior. And for the line, we only care about its interior and boundary. I found this in the PostGIS documentation, "Using PostGIS: Data Management and Queries" 1

``````                 Interior           Boundary           Exterior
Interior   dim( I(a) ∩ I(b) )  dim( I(a) ∩ B(b) )  dim( I(a) ∩ E(b) )
Boundary   dim( B(a) ∩ I(b) )  dim( B(a) ∩ B(b) )  dim( B(a) ∩ E(b) )
Exterior   dim( E(a) ∩ I(b) )  dim( E(a) ∩ B(b) )  dim( E(a) ∩ E(b) )
``````

If we check the intersection of a line (a) with a point (b), we only care about the 1st and 4th checks (reading left to right, top to bottom).

1. Does the interior of the line (a) intersect the interior of the point (b)?
2. Does the boundary of the line (a) intersect the interior of the point (b)?

You got back False for both, so the line doesn't intersect the point.

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i did not understand it yet completely. i am trying to come in chat room but fail .. i do't know whats the problem for logging to chat room.. – tina Nov 25 '10 at 0:40
anyhow... point have interior .. so line and point have relation in case of interior so there must be T in 1st index of matrix.. same as point have no boundry so no relation exist b/w point and line case.. it must be F in 2nd index sane as for exterior it msut be F..finally in my point of view, notation msut be TFFTFFTFF.. please put light on it ... – tina Nov 25 '10 at 0:42
well if i consider F**F***** where F means no relation but as we know that point interior and line interior haev relation.. so why there is F.. – tina Nov 25 '10 at 0:48
why i did not use TFFTFFTFF instead of F**F***** – tina Nov 25 '10 at 0:52
F**F*****.. since here line have exterior and point have interior than why index 7 there is *.. it should be F or T – tina Nov 25 '10 at 8:15

That document is confusing to read but it is consistent. Its definitions on p. 2 all rely ultimately on the "definition" of boundary, which is not a definition at all ("The boundary of a geometry object is a set of geometries of the next lower dimension"). (I suspect it is intended to be a continuation of one or more of its references.) The only clear thing is that the boundary of a "geometry" must have a lower dimension. Therefore, because the dimension of a point is zero,

• The dimension of a point's boundary must be -1 (empty).

• Whence, because "the interior of a geometry object consists of those points that are left (inside) when the boundary points are removed," the "interior" of a point must be the point itself, because that is what remains when you remove an empty set from a point.

The reason for requiring that a boundary have lower dimension originates with simplicial homology theory, where things like "geometries" do have effective definitions and the operation of taking the boundary of a simplicial complex is fundamental.

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ok i am still not understanding.. as i know that point have no interior .. it jsut have boundry/.. So this notation F**F***** .. what it does mean? – tina Nov 24 '10 at 5:16
(1) It is correct that points have empty interiors in the sense of "interior" used in metric spaces, but this sense is different. You have to rely on the "definitions" supplied in the paper, not on what you already know. In this paper a point's boundary is empty and its interior is nonempty. (2) The notation is defined at the bottom of p. 6, except there's a typographical error: "T" means the intersection is not empty. – whuber Nov 24 '10 at 5:24
how and why we are using this notation F**F***** ..according to the defination in paper, notation should be TFTTFTTFT... this because point have interior so relation exist b/w point and line similar point have no boundary so relation will be F.. please do clear to me about the notation – tina Nov 24 '10 at 5:30
any one cna explain me this FF*****. it shoule be like TFTTFTTFT.. why it s FF*****. – tina Nov 24 '10 at 12:40