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Thread View: sci.math.num-analysis
2 messages
2 total messages Started by Han de Bruijn Wed, 30 Sep 1992 10:11
Re: Points in Polygons
#671
Author: Han de Bruijn
Date: Wed, 30 Sep 1992 10:11
52 lines
3226 bytes
In article <1992Sep27.022750.8620@leland.Stanford.EDU> Laurence James Edwards:
> Wow! I had forgotten what a godly book Preparata&Shamos is.

In article <1992Sep28.083843.23616@dutrun2.tudelft.nl> Han de Bruijn:
> Bad taste.

In article <1992Sep28.231335.10973@leland.Stanford.EDU> Laurence James Edwards:
> While I wouldn't recommend it for recreational reading, Preparata&Shamos does
> present a comprehensive and coherent account of computational geometry,
> and I think it is the first book devoted to the subject.

Trivialiter, because Preparata&Shamos are the _inventors_ of "Computational
Geometry". Same story with "The Fractal Geometry of Nature", by Mandelbrot,
which is, equally trivialiter, the "first" book about fractals.

Actually, the stuff covered by Preparata & Shamos IMNSHO barely justifies the
creation of a new, separate, area of investigation. A most important part of
it (Voronoi tesselation) is nothing new & belongs to classical mathematics.

In article <5C1-w=_@engin.umich.edu> Samer Takriti:
> I have received many answers referring to "Computational Geometry,
> an introduction" by Preparata and Shamos. Thanks.
> It looks to me that he methods proposed by this book can be applied
> in R^2 only. Applying these methods in higher dimensions would 
> increase the complexity of the algorithm (exponential complexity).

The book doesn't contain obvious generalizations to multiple dimensions
in the first place. Even worse. Solutions in 2-D are presented in such a
way that a generalization from that point to, say, three dimensions is
made impossible beforehand. One shouldn't use specific properties of the
plane (like orientation of angles) in a theory that could be generalized
to three and more dimensions. Overall, the attacks presented in the book
are quite unprofessional. Any experienced programmer could do better.

Godly book? You know what godly books are? Here is a list of my ultimate
favorites:

- "The Feynman Lectures on Physics, part III"
- "The Theory of Radiation" by Max Planck
- "The Special Theory of Relativity" by Albert Einstein
- "Relativity Reexamined" by Leon Brillouin
- "Le phenomene humaine" by Teilhard de Chardin
- "Das Kapital, part 1" by Karl Marx
- "Buitenaardse Beschaving" by Stefan Denaerde
-  And, oh well, The Bible itself ...

Preparata&Shamos, or Mandelbrot, will never be in that list.
-- 
* Han de Bruijn; Applications&Graphics | "A little bit of Physics * No
* TUD Computing Centre; P.O. Box 354   | would be NO idleness in  * Oil
* 2600 AJ  Delft; The Netherlands.     | Mathematics" (HdB).      * for
* E-mail: Han.deBruijn@RC.TUDelft.NL --| Fax: +31 15 78 37 87 ----* Blood
Re: Points in Polygons
#686
Author: Laurence James Edwards
Date: Wed, 30 Sep 1992 22:16
57 lines
3384 bytes
In article <1992Sep30.101144.11382@dutrun2.tudelft.nl>, rcpshdb@dutrun2.tudelft.nl (Han de Bruijn) writes:
|> In article <1992Sep27.022750.8620@leland.Stanford.EDU> Laurence James Edwards:
|> > Wow! I had forgotten what a godly book Preparata&Shamos is.
|> 
|> In article <1992Sep28.083843.23616@dutrun2.tudelft.nl> Han de Bruijn:
|> > Bad taste.
|> 
|> In article <1992Sep28.231335.10973@leland.Stanford.EDU> Laurence James Edwards:
|> > While I wouldn't recommend it for recreational reading, Preparata&Shamos does
|> > present a comprehensive and coherent account of computational geometry,
|> > and I think it is the first book devoted to the subject.
|> 
|> Trivialiter, because Preparata&Shamos are the _inventors_ of "Computational
|> Geometry". Same story with "The Fractal Geometry of Nature", by Mandelbrot,
|> which is, equally trivialiter, the "first" book about fractals.

Well the term, Computational Geometry, was first applied to this
particular field of study in a 1975 paper by Shamos. The book is
copyright 1985, so it is not trivially evident that it would be the first
book on the subject.

|> Actually, the stuff covered by Preparata & Shamos IMNSHO barely justifies the
|> creation of a new, separate, area of investigation. A most important part of
|> it (Voronoi tesselation) is nothing new & belongs to classical mathematics.

I didn't realize they did big oh analyses of algorthms in classical
mathematics.

|> The book doesn't contain obvious generalizations to multiple dimensions
|> in the first place. Even worse. Solutions in 2-D are presented in such a
|> way that a generalization from that point to, say, three dimensions is
|> made impossible beforehand.

That simply is not true. For example, convex hull algorithms are generalized
to n-dimensions, and there are a number of sections on extending 2-D results
to higher dimensions.

|> One shouldn't use specific properties of the
|> plane (like orientation of angles) in a theory that could be generalized
|> to three and more dimensions.

I assume you mean the point in polytope problem here. The theory is
not about general algorithms that work in all dimensions but about worst
case analysis for a given problem. The authors point out that very
little is known about point location problems in E^3 and higher dimensions.

|> Overall, the attacks presented in the book
|> are quite unprofessional. Any experienced programmer could do better.

Ahem, "unprofessional"? First off, the book is *an introduction*. Second,
they do not claim to present professionally written code, the point
of the book is the theoretical worst case analysis of possible algorithms
answering a number of related geometric queries. Big oh worst case analysis
does not always lead to algorithms well suited for a particular application,
the authors specifically admit that.

Larry Edwards
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