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RSS >  3 Point Cap - A Math Problem, How to get the exact dimensions?
zapp #1 19/07/2010 - 13h16

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Hi!

I built myself a 3-Point-Cap from an old baseball hat, and it works really well.

Now, to get the most out of it, I want to give FreeTrack its exact dimensions.

My problem is, I can only measure two sides (b,c) and calculate a third one (a).
I am no math genius, but I am stuck with two variables (x,y) that are codependent, but can be anything between zero and a because I don't know any angles and I don't see any solution to this.

Posted Image

So how do you get the most accurate values for x and y, which you have to enter in FreeTrack?
Any ideas?

Since the cap is in my way, simply using a ruler is not sufficient.

Cheers,
Zapp
slaver1 #2 20/07/2010 - 09h54

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You need to know one more angle in triangle axy.
dewey1 #3 20/07/2010 - 14h15

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I get about 93mm for X-axis and 112mm for the Y-axis. (Tolerance of .5mm)
This was determined by CAD program with an assumption of brim to top of 112mm.
Can you get an approximate measurement of brim to top?
Edited by dewey1 on 20/07/2010 at 16h30.
zapp #4 21/07/2010 - 08h55

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@slaver1
Are you sure this link was meant for me?
Because I have Win7 x64 and run FreeTrack 2.2.0.279 with a Microsoft VX3000 Camera and have absolutely no problems with it... I'm rather amazed how well it works :)

@dewey1
Thank you!
That's exactly my problem. The only formula I know to calculate x and y is x²+y²=a² when I measure one side and calculate the other, I end up with a range of more or less

x ~ 95 to 115 and
y ~ 90 to 110mm

So yeah, I guess you can say I suck at using a ruler ;)
dewey1 #5 21/07/2010 - 16h27

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Here are three 3D models with variable heights and corresponding X-axis.
I am sure one of these should be close enough!

Posted Image
slaver1 #6 22/07/2010 - 07h11

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@slaver1
Are you sure this link was meant for me?
Because I have Win7 x64 and run FreeTrack 2.2.0.279 with a Microsoft VX3000 Camera and have absolutely no problems with it... I'm rather amazed how well it works


No. Link is just in my sig..... ;D
zapp #7 27/07/2010 - 08h36

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@slaver1
Ups. I totally didn't see your comment before ;)

But in the meantime I figured out that measuring one side and calculating the other one makes the error even worse. So I went to get some Chinese food the other day, built myself some right angles out of chopsticks and measured my entire head with them... and it really makes a difference in FreeTrack.

So I recommend to anyone to spend some time into measuring your devices, because now, my head-movements are much more accurate than before :)

Thanks for the help!
Edited by zapp on 27/07/2010 at 08h37.
dewey1 #8 27/07/2010 - 08h45

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zapp

What were the final dimensions used for your data into freetrack?
zapp #9 28/07/2010 - 11h01

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I went with x=112 and y=102, which leaves me with an a=151.

But given the fact that I based my calculations for x and y on a value which already added two possible measuring errors, I am not surprised that the (hopefully) real values do not match the calculated ones.

x     y     c
103   103   146
104   102   146
105   101   146
106   100   146
107    99   146
108    98   146
109    97   146
110    96   146
111    95   146
112    94   146
113    92   146


And what I have learned from all this is, that Error Propagation really works and chopsticks are better than math :)
dewey1 #10 28/07/2010 - 13h12

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zapp;

You can't fault the math. The real problem was the accuracy of the individual measurements. A tolerate of 10% is fairly large. If you had a 1% tolerance in your measurements, the results would have been much better.

Here is the 3D model with your latest measurements.


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