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Topic: What does one call vector geometry without a coordinate system?
Replies: 32   Last Post: Sep 9, 2013 4:45 PM

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fom

Posts: 1,969
Registered: 12/4/12
Re: What does one call vector geometry without a coordinate system?
Posted: Sep 2, 2013 7:46 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 9/2/2013 3:24 PM, FredJeffries wrote:
> On Saturday, August 31, 2013 3:28:21 PM UTC-7, fom wrote:
>>
>> I like what is in the link you posted. It clarifies
>> many details for me. It differs from Bowen's presentation
>> in that it presents an affine space in terms of a
>> faithful group action.
>>
>> f: ExV -> E
>>
>> where I have used V for the translation space.
>>
>> In Bowen, one has
>>
>> f: ExE -> V
>>
>> Although I would have to compare the presentations
>> more carefully to appreciate any subtle differences,
>> Bowen's view seems to be directed toward the topological
>> constructions about to be discussed in his presentation.

>
> There could be something to that. The other paper seems
> to come from Jean Gallier's class notes for a computer
> science course "Geometric Methods in Computer Science"
>
> http://www.cis.upenn.edu/~cis610/home09.html
> http://www.cis.upenn.edu/~cis610/cis610-notes-09.html
> http://www.cis.upenn.edu/~cis610/cis610-syllabus-09.html
>
> "The purpose of this course is to present geometric
> methods used in computer vision, robotics and computer graphics."
>


I think that the distinction for computer
visualization is to make clear the relationship
of affine aspects and projective aspects so
that they can be treated properly in algorithms
implementing the graphics. Visualization essentially
corresponds with projective methods because of
perspective drawing.

Look at the responses to me from Seymour. Bowen is
going directly to Euclidean spaces. His mention of
affine spaces is secondary. The text is using inner
product spaces, and, this is what will be required
to introduce the general distance function in the
next few pages. This is what Seymour's correction
to my statements reflect.





Date Subject Author
8/30/13
Read What does one call vector geometry without a coordinate system?
lite.on.beta@gmail.com
8/30/13
Read Re: What does one call vector geometry without a coordinate system?
Tanu R.
8/30/13
Read Re: What does one call vector geometry without a coordinate system?
William Elliot
8/30/13
Read Re: What does one call vector geometry without a coordinate system?
Brian Q. Hutchings
8/31/13
Read Re: What does one call vector geometry without a coordinate system?
fom
8/31/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
8/31/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
lite.on.beta@gmail.com
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Peter Percival
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Brian Q. Hutchings
9/3/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/3/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/3/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/4/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/4/13
Read Re: What does one call vector geometry without a coordinate system?
fom
9/4/13
Read Re: What does one call vector geometry without a coordinate system?
Brian Q. Hutchings
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Shmuel (Seymour J.) Metz
8/30/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
JT
9/1/13
Read Re: What does one call vector geometry without a coordinate system?
Ken.Pledger@vuw.ac.nz
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
lite.on.beta@gmail.com
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
Ken.Pledger@vuw.ac.nz
9/3/13
Read Re: What does one call vector geometry without a coordinate system?
lite.on.beta@gmail.com
9/9/13
Read Re: What does one call vector geometry without a coordinate system?
FredJeffries@gmail.com
9/2/13
Read Re: What does one call vector geometry without a coordinate system?
Narasimham

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