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

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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

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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.

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1/15/2010 9:36:37 PM