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.
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