[R] Centre of gravity of a mountain

[Nordlund, Dan (DSHS/RDA)]

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of Peter Langfelder
> Sent: Tuesday, November 09, 2010 3:49 PM
> To: Barry Rowlingson
> Cc: r-help at r-project.org; Ab Hu
> Subject: Re: [R] Centre of gravity of a mountain
> 
> On Tue, Nov 9, 2010 at 3:40 PM, Barry Rowlingson
> <b.rowlingson at lancaster.ac.uk> wrote:
> > On Mon, Nov 8, 2010 at 5:15 PM, Peter Langfelder
> > <peter.langfelder at gmail.com> wrote:
> >
> >> If you also need the z coordinate, it simply the mean of the matrix
> Z.
> >>
> >> zCenter = mean(Z)
> >
> >  How can that be right? Suppose your mountain is very flat, so that
> > your mountain is effectively a cube. The Z values are all the same,
> > and so their mean is the same. However the centre of mass is, by
> > symmetry, clearly at height/2.
> >
> >  Similarly suppose your mountain matrix is one large cell value and
> > all the rest are near zero - the mean Z will be close to zero but the
> > centre of mass will be almost half way up the single cell value,
> > because all the near-zeros contribute nothing to the centre of mass
> > position.
> 
> Yup, the z coordinate is wrong. Only the x and y are right.
> 
> Peter
> 

I believe that should have been mean(z)/2

Dan

Daniel J. Nordlund
Washington State Department of Social and Health Services
Planning, Performance, and Accountability
Research and Data Analysis Division
Olympia, WA 98504-5204