It took me way longer than it should have and I don't know how to round up the edges but here goes an initial rough model of the blade using two arb6 primitives.
2017-07-17 16:37 GMT+02:00 Mario Meissner <mr.rash....@gmail.com>: > Hello Sean. > > In the general case, we do not necessarily know the “shape" of the >> geometry, particularly having an equation for the geometry to substitute in >> a line equation like in your case. For example, the sword blade case might >> be constructed as a union of several objects, like if you model this >> example: http://www.shopwingchun.com/ewcblog/uploads/blade-tapers.jpg >> >> That would make for a really good simple test case! Try and model either >> of them. >> >> > Good idea to have a test case like this one that is not as straightforward > as as a box :). Will start modeling it! > > >> Instead of considering the ray line, whose intersection with geometry is >> already covered in a *_shot() function, consider line segments. Basically, >> sets of in/out points (segments) are what you get during geometry >> evaluation. Example of two segments (s0 and s1) with two in-points (t0 and >> t2) and two out-points (t1 and t3): >> >> s0 s1 >> o———————————o o———————o >> t0 t1 t2 t3 >> >> With segments, it begs for some function that says — for a given object — >> what the density is at point t2, for example, or what the density is from >> t1 to t2 and t2 to t3. If calling code knows the density goes from 0.1 at >> t0 and 0.5 at t1, then it can integrate to know the average density is 0.3 >> and represents a 3D mass of XXX*0.3 mm^3. >> >> What’s missing is a density specification that, given t0, t1, or both, >> can report the 0.1, 0.5, or 0.3 values. >> >> The simplest starting point that comes to my mind would be simple 3D >> density points that are interpolated. Something like this becomes >> relevant: http://docs.qgis.org/2.2/pt_PT/docs/gentle_gis_introduction/ >> spatial_analysis_interpolation.html > > >> >> > • For this new example box, I would define the density in >> language-agnostic terms or pseudo-code as the following: >> > set box origin density 3; >> > 1,0,0 linear density 5; >> > 0,1,0 linear density 6; >> > 0,0,1 linear density 1. >> >> I think this is on the right track for density specification. The >> important bits are that we define a set of 3D points, a density at each >> point, and an interpolation method for in between. Lets keep it that >> simple. >> > > You suggest that instead of having an exact function like I proposed, we > should specify a set of segments with their densities and interpolations? > If I'm understanding you correctly, we should let the user define any > arbitrary number of segments in a manner that is similar to the pseudo-code > I wrote, and this set of segments should then be somehow managed in a way > that the calling code can request the information about those (and any > other as well?) segments of the material? > > If we used my function, we could technically extract the information we > need about those segments, don't we? The start and end points are > straightforward, as that's what the function returns. We just feed it the > coordinates. For the interpolation, we just need to take the derivative > alongside the segment to see how it behaves (I guess this could be the > problematic part). But transforming the information the user gives through > those commands into a function, and then extracting it again out of the > function may be an unnecessary step, I realize. > > >> > Here I would read it in natural language like: >> > At the origin the density of the box is 3. If we go towards 1,0,0 we >> will find that the density changes linearly until it is 5. If we go towards >> 0,1,0 it will change linearly until it is 6... etc. >> >> Agreed, this is good! Only suggestion I think would be to normalize the >> values into a 0.0 to 1.0+ range as a density multiplier. This way, would >> could apply the same distribution to different materials. It will also >> avoid having conflicting specifications. We can still say “this is bone” >> which has 1.75 g/cm^3 and which would equate to a 1.0 density function >> value. What do you think? >> > > Yes, good idea. So there are two elements here: material and density > distribution?. Density distributions are normalized and can be applied to > many materials, each one with a different base density. Nice! > > As an aside, here’s a nifty real-world application where we might instruct >> a 3D printer to adjust the density of a car’s frame (e.g., the density of >> some internal lattice structure) based on how rigid that part of the frame >> needs to be: https://ucarecdn.com/1e2fd4d4- >> da99-41e0-86ff-3f357dab8181/-/preview/1440x1080/ >> >> For that case, you’d pick any one of the densities as your normalized >> density (or use the density of the plastic being used), and then have a 3D >> point cloud specifying the densities of various zones. >> > > Interesting! This could be an advanced example case. Looks difficult to > model though. > > Mario. > >
blade.g
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