Square to a circle?

Thread Starter

spinnaker

Joined Oct 29, 2009
7,830
I downloaded some meter face design software.

http://www.tonnesoftware.com/meter.html

The software has a whole bunch of parameters for the dimensions of your meter. Two of those dimensions are height and width. But the software assumes a square meter face. Mine our round.

I made may first found and things are pretty close but the scale is two wide. One of the dimensions is space between the screw holes. This measurement matches perfectly to my actual meter face.

I could go trial and error but I was wondering if there is a way to figure this out mathematically.
 

wayneh

Joined Sep 9, 2010
17,498
Of course there is, but personally I’d need a better description of the problem. Trial and error may be faster!
 

Thread Starter

spinnaker

Joined Oct 29, 2009
7,830
Of course there is, but personally I’d need a better description of the problem. Trial and error may be faster!
Not sure how I could explain it any better. Software expects to draw a square but I have a circle. I need to fit the square inside the circle, at least from a width standpoint.
 

WBahn

Joined Mar 31, 2012
30,088
A square, or a rectangle?

If you need a square to just fit inside the circle and you have a circle of radius R, then the width (and height) of the square is simply √2·R.

If you want to use a rectangle of dimensions WxH, then W² + H² = 4R²
 

Papabravo

Joined Feb 24, 2006
21,228
What you want is called a conformal mapping. You want to map a rectangle into a section of an annular ring.
Slightly more exotic, would be to map the rectangle onto an elliptical annular ring.
You could also do the layout in polar coordinates.
 

wayneh

Joined Sep 9, 2010
17,498
Not sure how I could explain it any better. Software expects to draw a square but I have a circle. I need to fit the square inside the circle, at least from a width standpoint.
Are you talking about an inscribed rectangle, or bending the rectangle to wrap around a ring as PB just described?
Either is a trivial chore in regular drawing programs.
 

WBahn

Joined Mar 31, 2012
30,088
It sounds like he just wants a circle circumscribed around the rectangle. I can't image how a conformal mapping would produce anything useful for what he seems to be describing.
 

Thread Starter

spinnaker

Joined Oct 29, 2009
7,830
I think it's this:
vs


I agree that trial and error is the way to do it.

Yep. I have the meter on the left but software expects meter on the right. What is happening is the ends of the scale are knocked off. Trail and error it is I guess.
 

wayneh

Joined Sep 9, 2010
17,498
Yep. I have the meter on the left but software expects meter on the right. What is happening is the ends of the scale are knocked off. Trail and error it is I guess.
Can you show an example or better yet attach a file that shows the problem? There could be some easy solutions from just image editing or drawing.
 

SLK001

Joined Nov 29, 2011
1,549
I've always done my meter faces in AutoCad. I used the original meter face as a template to measure all the particulars.
 

Picbuster

Joined Dec 2, 2013
1,047
X axis = V sin(Q)
Y axis = V cos (Q)
This will produce a circle when q goes from 0 to 360 in steps of 1
Take 4 steps 0-90-270 -360 you produce a square.
Take 3 steps triangle.
V is vector ( radius)
Q in degree.

Picbuster
 

WBahn

Joined Mar 31, 2012
30,088
Yep. I have the meter on the left but software expects meter on the right. What is happening is the ends of the scale are knocked off. Trail and error it is I guess.
Have your tried using the scaling I gave you? It might at least get you a good starting point.
 

Thread Starter

spinnaker

Joined Oct 29, 2009
7,830
Have your tried using the scaling I gave you? It might at least get you a good starting point.

I ended up using the trail and error method. At first I thought the software would size the scale for you bases off of the dimensions you but in for the meter but that is simply not true. The two main settings are deflection and actual virtual offset. Deflection is basically the arc of the scale. Offset is where the center of the "circle" is from the bearing.

What I did was to get it close printing to paper. I then dialed it in closer by printing to wax paper (I use wax paper in thermal transfer). Wax paper makes it easy to line things up.

I just printed to a piece of paper here but what I will probably end up doing is to use thermal transfer to transfer the scale to the metal backing plate.

upload_2017-10-19_17-52-9.png
 
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