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how to calculate shortest distance between two point on a surface

Could anyone suggest me methods on how to calculate shortest distance
between two point along a surface. The surface is not standard one
like sphere.
Thanks.
0
1/15/2010 4:27:29 PM
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In article <34590a0b-3ceb-456d-93ae-522b32dec017@c3g2000yqd.googlegroups.com>,
Arkward  <sunjigang1965@yahoo.com.cn> wrote:
>Could anyone suggest me methods on how to calculate shortest distance
>between two point along a surface. The surface is not standard one
>like sphere.
>Thanks.


Why do you want to know? I use to have students construct geodesics
numerically via matlab, but calculus of variations can get analyitical
solutions of the minimal geodesic at times. 
-- 
Steven Bellenot                 http://www.math.fsu.edu/~bellenot
Professor and Associate Chair               phone: (850) 644-7405 
Department of Mathematics                        office: 223 Love
Florida State University          email: bellenot at math.fsu.edu
0
fakeuser
1/15/2010 5:40:04 PM
On Jan 15, 8:27=A0am, Arkward <sunjigang1...@yahoo.com.cn> wrote:
> Could anyone suggest me methods on how to calculate shortest distance
> between two point along a surface. The surface is not standard one
> like sphere.
> Thanks.

You want a "geodesic". See, eg.,
http://www.maplesoft.com/applications/view.aspx?SID=3D34940&view=3Dhtml
(which deals directly with this problem in a Maple framework) or
http://mathworld.wolfram.com/Geodesic.html (general theory) or
http://www.physicsforums.com/showthread.php?t=3D169560 (some examples).

R.G. Vickson
0
Ray
1/15/2010 5:43:06 PM
On 15 Jan, 17:40, fakeu...@invalid.domain wrote:
> In article <34590a0b-3ceb-456d-93ae-522b32dec...@c3g2000yqd.googlegroups.=
com>,
>
> Arkward =A0<sunjigang1...@yahoo.com.cn> wrote:
> >Could anyone suggest me methods on how to calculate shortest distance
> >between two point along a surface. The surface is not standard one
> >like sphere.
> >Thanks.
>
> Why do you want to know? I use to have students construct geodesics
> numerically via matlab, but calculus of variations can get analyitical
> solutions of the minimal geodesic at times.
> --
> Steven Bellenot =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0http://www.math.fsu.edu/~b=
ellenot
> Professor and Associate Chair =A0 =A0 =A0 =A0 =A0 =A0 =A0 phone: (850) 64=
4-7405
> Department of Mathematics =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0 =A0=
office: 223 Love
> Florida State University =A0 =A0 =A0 =A0 =A0email: bellenot at math.fsu.e=
du

Thank you for your advice.
In an algorithm, distance between two points of data set is shortest
graph distance as an approximation of geodesic distance. I plan to
simulate the surface by aggression then calculate the geodesic
distance on the simulated surface.
0
Arkward
1/15/2010 9:36:37 PM
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