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diagonal of irregular object

Posted on 2013-12-28
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Last Modified: 2014-01-02
hy ,
have excel sheet that randomly calculates lengths of  8 sided object ,
i need to calculate diagonal of the object.
here is example

example
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Question by:thmh
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13 Comments
 
LVL 84

Expert Comment

by:ozo
ID: 39743445
I can't resolve the shape of the object from that image, but if it is a box with rectangular sides, then the diagonal would be sqrt(length^2+width^2+height^2)
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Expert Comment

by:teylyn
ID: 39743453
It might help if you could post an image that shows the content in a bit more than a stamp size on a huge sheet. Use the snipping tool and resize the image to remove the white space. Then attach it.
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LVL 84

Expert Comment

by:ozo
ID: 39743456
It may also help if you could indicate which lengths you know, and which diagonal you wish to calculate.
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Expert Comment

by:Technodweeb
ID: 39743546
gb = sqrt(hg^2)+(sqrt((ah^2)+(ab^2)))

That should do it...
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Author Comment

by:thmh
ID: 39743826
ok , here is new picture ,
and Technodweeb can you explain your formula
example
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LVL 11

Expert Comment

by:Technodweeb
ID: 39743855
If all corners are 90 degrees then you can take the hypotenuse of the bah which is segment bh. Then take that length as part of the bhg to calculate the hypotenuse segment gb.

If the 8 corners are not 90 degrees, then I do not think my calculation will work as is.

By the way, the object you have drawn has only 6 sides and not 8 as you originally described. Are you wanting 6 sides or 8?

Then again this could be a big illusion for me...
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Expert Comment

by:ozo
ID: 39743857
If bah and bhg are right angles, my previous answer holds.
If the object is irregular, more information would be needed to determine gb.
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Author Comment

by:thmh
ID: 39744545
my mistake it's 6 sided irregular object , not 8 ,
there are all irregular triangles no 90 degrees corners and all lengths are known

object
so is there formula
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Expert Comment

by:ozo
ID: 39744558
I still don't think that's enough information.
Even if the sides are known to be planar, which does not appear to be the case in your example,
then with lengths ab=bc=cd=da=be=ef=fc=fg=gh=he=dg=ah=1
you could end up with bg anywhere between 0 and 3 by changing the angles at each corner.
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Assisted Solution

by:Technodweeb
Technodweeb earned 150 total points
ID: 39744710
Without some angle information, I am afraid the only way to solve would be to approximate. I cannot come up with any mathematical formula to define any of the corner angles which will be required to solve for the diagonal gb.
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Accepted Solution

by:
ozo earned 150 total points
ID: 39748382
There is not enough information to determine gb
The following sets of points have very different gb distances,
despite both satisfying the other specified lengths

a = (0.000000,0.000000,0.000000)
b = (12.000000,0.000000,0.000000)
c = (4.310529,2.207268,0.000000)
d = (7.500000,2.218751,6.231143)
e = (9.457264,4.313399,-4.891736)
f = (7.456191,0.706988,1.963153)
g = (12.000000,0.000000,0.000000)
h = (6.000000,8.533921,3.488867)


a = (0.000000,0.000000,0.000000)
b = (12.000000,0.000000,0.000000)
c = (6.791680,6.072348,0.000000)
d = (3.013889,7.662736,5.674413)
e = (5.097953,1.161319,0.114379)
f = (4.187521,9.108522,0.000000)
g = (0.932321,12.903739,0.000000)
h = (3.125778,6.259707,8.487967)
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LVL 27

Assisted Solution

by:tliotta
tliotta earned 100 total points
ID: 39750456
A frame can be constructed with tubes cut to the given lengths and connected with threads through the tubes tied at the corners. Having a physical model like that would demonstrate why it's not possible to calculate a diagonal with only the lengths of the edges known.

Such a frame is not rigid. It can be moved in all directions to cause the length of the diagonal to grow or shrink.

Now, once a solid interior exists, the diagonal becomes fixed. But the angles all become fixed at the same time. It's only when both the edges and the angles become fixed at the same time that the diagonal has a known length. The edges alone are not enough.

Tom
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Author Closing Comment

by:thmh
ID: 39750970
so calculating diagonal is to complex or even impossible , will try another approach (question)
 tnx
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