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- From: rcskb@minyos.xx.rmit.oz.au (Kendall Bennett)
- Newsgroups: comp.graphics
- Subject: Re: Simple Convexity Working Group (preliminary report)
- Date: 9 Nov 1992 01:58:44 GMT
- Organization: RMIT Computer Centre
- Lines: 78
- Message-ID: <1dkgkkINNj14@escargot.xx.rmit.OZ.AU>
- References: <720421504.10@freudsys.nl.mugnet>
- NNTP-Posting-Host: minyos.xx.rmit.oz.au
-
- Kenneth.Sloan@freudsys.nl.mugnet.org (Kenneth Sloan) writes:
-
- >Organization: CIS, University of Alabama at Birmingham
-
- >>...A polygon is either
- >>convex, or non-convex.
-
- >Is the following polygon "convex"?
-
- >0 0
- >1 0
- >1 1
- >0 0
- >1 0
- >1 1
-
- In my books it definitately is. It is not simple, but it is convex. Why
- would you ever need to handle this sort of poly except in dicussions about
- whether they are convex or not?
-
- >>... Mathematical definitions of convex polygons abound,
-
- >Please supply a pointer to an unambiguous, complete, authoritative
- >definition. Definitions of convex sets abound. Polygons (as we have
- >been treating them) , on the other hand, are *boundaries* - not the
- >interior. The *path* of the boundary curve counts just as much as the
- >set of points enclosed by the boundary.
-
- Polygons are generally used to model the set of points contained within
- the polygon boundary. How do you think you get the definition of which
- pixels to draw for self intersecting polygons? Convex sets are bounded
- by convex polygons. In the paper that I mentione by Chazelle and Dobkin,
- a good defintion of a convex polygon is given. Obviously not complete
- and authoritative, since you would naturally find some counter example
- which no-one would ever see in practice.
-
- >>so why the need to say that it is convex and SIMPLE? If it is convex, it
- >>MUST be simple.
-
- >Oh really? See the polygon above. Is it "convex"? Is it simple? How
- >about this one:
-
- Ok, so it may be non-simple but still convex as in the above example.
-
- >0 0
- >2 0
- >1 2
- >1 1
- >1 2
-
- >Is it convex? Is it concave? Is it simple?
-
- It is concave. It is also simple in my books. It has two co-incident edges
- in it bounding an empty set of points, but if your traces it's border
- it is concave (ie: non-convex, you could scan convert this poly with a
- general polygon scan conversion routine).
-
- >> If it is not convex, then it must be concave.
-
- >Why is it necessary to bring in the concept of "concave"? We started
- >with "convex", and "simple", and constructed two classes: "convex and
- >simple" and "not convex or not simple". Why do you need "concave"?
-
- You don't. But why can't you simply say convex or not convex?
-
- >By the way...we're still waiting for your code.
-
- Yeah well, it is all hot air at the moment. I haven't had time to work
- on it, and I don't know when I will. Choose a winner without me :-)
-
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- | Kendall Bennett | Internet: |
- | RMIT Advanced Computer Graphics Centre | kjb@citri.edu.au |
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