> On Jul 19, 2017, at 7:04 AM, Mario Meissner <mr.rash....@gmail.com> wrote: > > We probably have some different ideas on how it should work, because of your > "the largest value should be 3*V=9". I thought that if we have a horizontal > vector going right, and a vertical vector going down, and we take the > diagonal that goes the full distance down and right (so basically a 2D square > where up left is origin and bottom right is point we want to calculate) the > result should be the combination of both multipliers.
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. > If the axis vectors were 3 right and 2 down, that point should have a > multiplier of 6 because it fully uses both axis vectors. From your statement > I assume that you didn't think of it this way. If you have a steel block that is density X in one corner, and 10 times that density (10*X) on the opposite corner, and 20*X on another corner, that implies the density will be in the X to 20*X range. You’re suggesting it would be in the X to… 200*X range. Nothing does that. Density factors don’t amplify — they combine linearly. It’s not necessarily even accurate to presume they are linear contributions from each point that can be summed up, but that’s a reasonable starting point that is easy to prove inductively for pure materials. 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. Cheers! Sean ------------------------------------------------------------------------------ Check out the vibrant tech community on one of the world's most engaging tech sites, Slashdot.org! http://sdm.link/slashdot _______________________________________________ BRL-CAD Developer mailing list brlcad-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/brlcad-devel
