> Attached goes an example of one way I think it might work.
This is an excellent example to work through!
> In the end we want one vector for each axis, that tells, through a
> multiplier, how the density changes as we move in its direction. Choosing any
> point in the region is taking the right combination of the vectors to go from
> the origin to the point, and applying the multipliers of the vectors to the
> density of the origin. Do this twice and you get in-point and out-point of
> the segment. Now you can interpolate and calculate mass.
I think I’m following you, but via different calculations. Where is your “3 +
3/2” coming from for segment a? I would have calculated it as a density field
going from 3 (pt V) to 6 (pt B), divided by the contribution ratio of each.
Showing all steps, undoubtedly with a mistake or three because this was done in
just a few minutes:
density(V) density(B) 3 6
———————–––––––––––– + ––––—––——–––––––––– = – + – = 4.5 = contrib(a1, VB)
vect(VB)/vect(a1'V) vect(BA)/vect(a1’B) 2 2
Obviously same result, but is that essentially the same method? What’s
throwing me is that I don’t get the same result for the out point, which means
I probably have something wrong. I get:
contrib(a2, VB) + contrib(a2, VA) 4.5 + 9
––––––––––––––––––––––––––––––––– = ––––––- = 6.75
2 2
Regardless, I’m not sure I understand how your result (10.5) is even possible
as the largest value should be 3*V=9, no?
> The user could also define non-axis vectors and we should then break them
> down into axis ones.
Yes, it’s important to note that geometry is often not axis-aligned like in
your setup, so deriving vectors from the points will probably be desirable.
That is, derive vectors VA, VB, VC, VD from the five density field points.
> This method only covers some really simple density distributions and fails to
> represent more complex ones like density values that go up and down as we
> advance in a certain direction. I see no easy way of modeling this without
> complicating the whole think a lot. What do you think?
This makes me think we’re using different methods. Summing contributions from
the different points/vectors should give values that go up and down…
Cheers!
Sean
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