Prism problem
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This animation from Wikipedia shows it's really very simple! (Inside a cube.)
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Good find jim.
Still quite a way out though
I also tried rotating a copy of the base triangle in to place by the dihedral angle (accurate to 6 decimal places) and that is still quite a way out as well. about 0.7% if i remeber correctly.
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Gee Jim,
That's indeed very simple!
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Unfortunately I have not found a solution for this problem in general (i.e. rotate/snap by pure construction), see attachment below.
For special cases like the one presented here by fruitjelly (a tetrahedron) there always seem to be good workarounds. So next question: How would you solve the rotation in the attached model to get the one and only edge AB?
(We had this discussion before about creating the perfect buckyball but that's also a special case)
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Ah, Wodan,
I remember this challange. I even have a "no-solution" version of this among my models at the WareHouse: http://sketchup.google.com/3dwarehouse/details?mid=8075be6a6da45be3d2f8fef8fa52eceb
Actually the exact same problem as here...
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Jim's image so far best illustrates the easiest way to for that shape. Then again, if ultimately, we want a equilateral triangle with for example 1m on each side.... We have to use maths, such as pythagoras theorem, but the weird never ending figures simply will not produce an accurate shape.
So do you guys think its ok to say that, as far as complicated geometry are concerned (especially with arcs and curves), sketchup ain't that useful when dealing with accuracy.
Modeling this tetrahedron had been a real pain, but turns out the solution is a damn cube....
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It's a known fact that SU accuracy isn't the best around, but then again it isn't meant for creating geometry smaller than the feet of a dust mite.
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@fruitjelly said:
Then again, if ultimately, we want a equilateral triangle with for example 1m on each side.... We have to use maths...
No we don't - we use the Tape measure tool. Make a triangle of any size, measure the side, and type the length you want, and press Enter. SU asks if you eant to resize the model, click OK, and you are done. If you have other things in your model that you don't want resized, group the triangle, and do the trick inside the group.
Anssi
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Even the cube method isnt entirely accurate, see my previous post.
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@remus said:
Even the cube method isnt entirely accurate, see my previous post.
really? i did the cube method 3 times and it always worked out perfectly.. every edge was the same length.. or maybe i'm not understanding something?
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Hmmm, perhaps i made a mistake when i did it, i'll give it a go when i get home.
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As long as we're looking things up on Wikipedia, we can see that it gives the dihedral (included angle between two adjacent faces) of a tetrahedron as 70.528779°. That gives us the following very simple construction:
~Voder
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@voder vocoder said:
As long as we're looking things up on Wikipedia, we can see that it gives the dihedral (included angle between two adjacent faces) of a tetrahedron as 70.528779°.
i think the challenge is to build the shape entirely using sketchup tools and locks.. the cube method makes this possible.. your solution uses math (albeit you went straight for the answer but 70.52....deg is a solution for an equation)..
here's an easy method for drawing an equilateral triangle without entering any numbers... [edit] - using this same method should work for for the entire shape but i'm having weird snap to problems.. i'll mess around with it tomorrow.. goodnight..
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I must have been doing something weird when i tried that cube method originally, works like a charm now.
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@remus said:
I must have been doing something weird when i tried that cube method originally, works like a charm now.
Okay Remus, a beer or two now for you or anyone else with %(#FF0000)[a correct method
with only SU, no math, to solve the problem attached to my previous post. No trial and error though,] I did that already. -
Wo3Dan, by what means did you place the guide point? What do you mean by "this could be endpoint A"?
~Voder
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@voder vocoder said:
Wo3Dan, by what means did you place the guide point? What do you mean by "this could be endpoint A"?
~Voder
Voder, interested in the beer, right?!!
I just placed a guidepoint (A’) on the vertical line, measured A’B and moved A’ up and/or down till I got the right length AB= 2102,833625??? mm From now on A’ is called A.
So this was done by trial and error, so to speak. And A is “only” accurate 6 decimals. Thereby it could be THE point A, the one I'm after.I want the red and yellow plane dimensions unchanged after rotation while they now have a common edge length AB=2102,833625xxx mm
But to be honest, I’m not really interested in being this precise. What I’m after is a decent
way to do a rotation/snap in any situation, something SU unfortunately seems to lack.
So a rotate/snap solely for the reason of better/easier 3D constructing.
Not everything is as regular as a tetrahedron.Wo3Dan
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@unknownuser said:
But to be honest, I’m not really interested in being this precise.
if you don't need super precision, you can use a heavily divided radius and it will get you pretty damn close if not right on the money..
2000 segments per circle here and the radii do in fact intersect..
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@wo3dan said:
Not everything is as regular as a tetrahedron.
True, including me, I'm afraid. But that's for a different forum.
@unknownuser said:
if you don't need super precision, you can use a heavily divided radius and it will get you pretty damn close if not right on the money.
2000 segments per circle here and the radii do in fact intersect.Jeff, I have taken your previous admonition to heart and agree that the purpose of these construction exercises is not just to get the job done by whatever means, but to work within the constraints of SU's tools and, by applying them in an ingenious and elegant manner, solve the construction problem. The tetrahedron-in-the-cube is such a solution, although no one here can take credit for it beyond finding it in Wikipedia. On the other hand, using a 2000-segment circle is not particularly elegant; rather, it's more of a brute force approach, wouldn't you agree?
Wo3Dan's problem is indeed vexing.
~Voder
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