
Why is 3D printing such a powerful way to make solid objects? - ph0rque
http://blog.reprap.org/2013/06/why-is-3d-printing-such-powerful-way-to.html
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pliny
>If you have some points round a 2D circle you can visit them in order one
after another; but if you have some points on a 3D sphere, there is no order
that places them one after another; and

Can someone clarify why this is true?

If we consider the sphere in spherical coordinates, we choose an arbitrary
starting point (as in the case of the 2D circle visit) them in the following
order: find the next point for which θ(pointA)-θ(pointB) (A is the point we
are now, B is the point we are considering) is minimal and greater than 0, if
there are two or more points that are the same number of radians away on the
θ-plane (and they are all minimal), find the point, out of those, for which
φ(pointA)-φ(pointB) is minimal and greater than 0, this uniquely identifies
all points on the surface of the sphere and allows us to order them if we have
some arbitrary starting point.

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te_platt
I don't think he meant it in a strict mathematical sense. Just that it's
easy/natural to pick a direction on a line and say point C is after A, and B
is in-between; whereas on a surface there isn't an obvious ordering.

~~~
starky
It however isn't difficult to do this for a 3-axis machine. in fact, the way
he describes building layer by layer is exactly how you make complex shapes on
a 3-axis mill. You essentially trace a line on the surface that you are trying
to machine. The problem simply reduces to the same line problem with the
points defined in 3 dimensions.

Of course, there are notable complexity benefits of 3D printing over 3-axis
machining, but many of them can be overcome with other machining methods such
as EDM.

~~~
mdturnerphys
"The problem simply reduces to the same line problem with the points defined
in 3 dimensions."

Except when you have overhangs.

~~~
starky
There are ways to deal with some of the overhang issues with proper tooling
though.

Regardless, as I said, 3D printing definitely wins in the complexity
capability, overhangs are just one of them.

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whatshisface
The math might be easier, but the physics is much harder. How do you 3D-print
a metal object? It's an easier bet to say that computing power will continue
to increase than it is to say some magical high temperature sintering process
will be made for home use.

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GregBuchholz
[http://www.shapeways.com/materials/steel](http://www.shapeways.com/materials/steel)

...of course if you don't want to deal with high temperatures, there is always
electrochemical deposition.

~~~
InclinedPlane
Sintered metals are never going to have the same properties that cast, forged,
and/or welded metals have. Such parts may be very strong compared to, say,
plastics, but there will always be a huge class of parts (especially for
machinery) which just cannot reasonably be made that way.

But that's fine, additive manufacturing doesn't have to be the end-all be-all
of manufacturing. People should concentrate more on leveraging the strengths
of 3D printing as much as possible rather than trying to make it be some jake
of all trades manufacturing tool that it can never be.

~~~
patrickyeon
> additive manufacturing doesn't have to be the end-all be-all of
> manufacturing

I agree with you, but thought I should point out that it may do more than you
expect. Here's a guy making rocket engines
[http://rocketmoonlighting.blogspot.com/2012/04/3d-printed-
ro...](http://rocketmoonlighting.blogspot.com/2012/04/3d-printed-rockets-cost-
curve.html) and one post older than this he's firing them.

~~~
twic
Impressive! It would be very interesting to see how the weight of his motors
compares to equally powerful motors made using traditional techniques.

