> I think I can follow you, but I'm not sure how to put contributions together.
> In the blade example you seem to be taking the mean value between them. I'll
> assume that's the case.
> Attached goes a simple box with two vectors. Should the density at point a be
> 5?
Let’s see. The gist of the original formula (which had a segment error in the
denominator, looking back) is to calculate the density contribution from VA,
the density contribution of VB, and then take their average (i.e., assume
simple linear contributions from each). Simple looking at your gridding
without any equations, we can see that:
contrib(a, VA) is 3.5
contrib(b, VB) is 6.5
Adding them up and taking the average is thus density 5. So yes. ;)
> Likewise, would point b have a density of 6 then?
Yes. 8 + 4 / 2.
> I'm not sure if I calculated the contributions correctly either, but this is
> the way that would make the most sense to me.
I think it’s as good a starting point as any and is relatively easy to
implement.
That said, note that this method does have a potential flaw in that we’re
treating the density contributions uniformly when in reality, they should
probably be weighted by distance to the vector.
In your example, they’re equidistant, so it works out. But consider the
implication of box that is 100 times taller, for example. Instead of 4 x 4,
it’s 4 x 400. Point b should be a value far closer to 8 than 4, certainly not
6. That’s a problem that can be dealt with later, but something to keep in
mind.
Cheers!
Sean
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