> This is flawed for one simple reason — material properties do not > multiply. At least, not for any common materials I can think of that we > care about. >
The problem lies in the definition I gave to the vectors. I tried to use them like follows: If we have a vector that goes to the right with multiplier 2, we need to multiply by 2 whenever we move towards the right, regardless of where we were before moving. This way combining multiple vectors results in multiplication. But it's not natural, as you say, so I've tried to understand the way you did it. > For example, consider a box that transitions from 0 to 1 density factor in > one dimension. The overall average density would naturally be half. Now > add a second transition from 0 to 1 in another orthogonal dimension. It’s > again half of what remained, one fourth overall. A solid aluminum cube > 1m^3 in size evaluates to 2700kg. Applying that density field, we should > see the mass drop to 675kg. > > The same holds for other shapes and fields. The density at any given > point is the linear summation across each vector’s contribution to that > point. Now there is a problem with more than one weight, but it would be > good to get a single simple linear density transition working first between > two points. > 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? Likewise, would point b have a density of 6 then? > 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 hope I'm getting closer to what you meant. Mario.
example_contributions.pdf
Description: Adobe PDF document
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