If you want the average density along the line of sight you could use the weight field "Ones", which would simply integrate the density as without a weight and divide it by the total path length.

Of course, it would be even simpler if you took the unweighted projection and divided it by the path length, as I just realized while writing this response. :)

On Jun 11, 2012, at 5:27 PM, Geoffrey So wrote:

Thanks for the explanations, but I think I'm still confused about something and want a bit more clarifications,

I thought when I'm projecting density, I'm doing (Density1 + Density2 +...), which is obviously wrong because I forgot about the Length dimention, so it should be:

Density1 * L1 + Density2 * L2 + ... = units of g/cm^2

When I'm projecting density with density as weight, I would think I would then be doing:

(Density1**2 * L1 + Density2**2 * L2 +...)/(Density1 + Density2 + ...) =  units of g/cm^2

But according to Sam, the units of weighted should be g/cm^3, where the role of v and w is switched.  "v": O(Density) is the value, and "w": O(Density)*O(L) is the weight.  And thus we get a projection weighted Density cell value in units of g/cm^3 instead of g/cm^2.  Shouldn't the weighting not change the units, or am I confusing projection weighted density with density weighted projection?

I've never done unweighted projections, so I kept using the units of the field (g/cm^3 in case of Density), those units seems right or have I been wrong all along?

From
G.S.


On Mon, Jun 11, 2012 at 1:32 PM, Sam Skillman <samskillman@gmail.com> wrote:
Geoffrey, if it helps, in the continuum limit, a weighted projection along the z direction is (v is the field, w is the weight):
Inline image 1
whereas unweighted is:
Inline image 4
For your example, the order of magnitude of your result would be O(density)**2*O(L)/O(density)*O(L) = O(density) for the weighted projection.  The unweighted is just O(density)*O(L).

Sam


On Mon, Jun 11, 2012 at 2:12 PM, Matthew Turk <matthewturk@gmail.com> wrote:
Hi Geoffrey,

On Mon, Jun 11, 2012 at 4:10 PM, Geoffrey So <gsiisg@gmail.com> wrote:
> Hi, sorry for asking a dumb question, but when I do a projection of density
>
> field = "Density"
> proj = pf.h.proj(direction, field, weight_field=field)
>
> the numbers I get are ~1e-28
>
> but when I do
> proj = pf.h.proj(direction, field, weight_field=None)
>
> the numbers become ~1e-4
>
> this is a 64 cube simulation, if I were to multiply 64 * 1e-28 for a
> projection with no weighting, shouldn't I still get numbers on the order of
> 1e-26 or 1e-27?  I'm guessing there's something I've misunderstood about
> pf.h.proj.  Am I missing like a CGS conversion factor when I don't weight it
> by some field?

Nope, weighting means to take the average with respect to some other
field.  So when you don't weight it, you don't take an average, you
get a line integral.  It's probably different by a factor of roughly
the same OOM as the number of centimeters your box is across.

-Matt

>
> From
> G.S.
>
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