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)
Ingeborg Hawighorst (Microsoft MVP / EE MVE)Microsoft MVP ExcelCommented:
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.
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?
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.
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.
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)
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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thmhAuthor Commented:
so calculating diagonal is to complex or even impossible , will try another approach (question)
tnx
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