How to determine offset when the length of the desired offset curve is known

Replies to This Discussion

Permalink Reply by djordje on January 18, 2014 at 9:34am

Hi Norm,

Your final curve (the one that has circumference 7 times larger than initial ellipse) is circle?
If that is so, than the solution of the problem is just in ellipse circumference formula. I took the fourth one(Infinite series 2) from here:

Attachments:

• ellipse_to_circle_circumference.gh, 7 KB

Permalink Reply by Norm Sash on January 18, 2014 at 9:44am

Thanks djorde... No, the outside curve is not a circle.  It is the curve that would result from taking the offset of the ellipse.  So the outside curve is not an ellipse, nor a circle -- it is the offset of an ellipse.  You can see what I'm doing in this attached gh. 

In the below image you can see the calculated ratio of offset curve to ellipse curve (6.661244).  What I need to determine is effectively the reverse... given an ellipse, and the resulting offset curve length (7x ellipse length), what is the offset value needed to get that desired offset curve length?

Attachments:

• Determining offset distance.gh, 13 KB

Permalink Reply by Norm Sash on January 18, 2014 at 9:56am

btw... thanks for the link to finding the length circumference of an ellipse.  I had no idea it was so complicated and exacting.  I just always cheat by using the Grasshopper "length" component :)

Permalink Reply by djordje on January 18, 2014 at 10:00am

Sorry for misunderstanding the type of the final shape.

If we leave out the equations, we could easily do this with Galapagos:

Attachments:

• ellipse_to_offset_ellipse.gh, 13 KB

Permalink Reply by Norm Sash on January 18, 2014 at 12:30pm

My gosh... thanks djordje!  I have never used Galapagos and didn't really know what it was for.  It worked great :)  It does take a little bit of time to run so it can be a somewhat slow model if doing many variations -- but sure is better than pick and shovel!

Thanks so much for your help.

Permalink Reply by Hannes Löschke on January 18, 2014 at 2:17pm

no need for galapagos... this is pretty straight forward with a little scriping

Attachments:

• ellipse_to_offset_ellipse.gh, 8 KB

Permalink Reply by Norm Sash on January 20, 2014 at 8:21am

Nice iterative process, Hannes.  And cool that you used the doc tolerance for the length fit tolerance. Thanks! 

Permalink Reply by Thomas on January 18, 2014 at 3:10pm

Hi Norm,
in this case you can calculate the right offset distance directly from the length of the ellipse.

The offset is 2*Pi*o longer than the ellipse (o = offset distance). In your example the offset has to be six times longer than the ellipse. So you can say:

2*Pi*o = 6*l        (l = ellipse length)

solve for o:

o = 3*l/Pi

You can do this with simple Grasshopper components:

Cheers!

Permalink Reply by Thomas on January 18, 2014 at 3:12pm

...and the definition

Attachments:

• ellipse_offset.gh, 7 KB

Permalink Reply by djordje on January 18, 2014 at 3:56pm

Nice Thomas.
What is the math behind the 2*Pi*o = 6*l ?

Danke.

Permalink Reply by Thomas on January 20, 2014 at 3:21am

Thanks!

I have calculated the circumference of the ellipse:

ellipseLength = 4*a*E(Sqrt(1-b^2/a^2)) = l

Then I calculated the length of the offset:

offsetLength = 2*Pi*o + 4*a*E(Sqrt(1-b^2/a^2)) = 2*Pi*o + l

Now we can say:

offsetLength = 7*ellipseLength
2*Pi*o + l = 7*l
2*Pi*o = 6*l

Permalink Reply by Norm Sash on January 20, 2014 at 8:57am

Excellent and elegant, TJO!  I plugged this in and it worked beautifully and quick.  And because of this my model is more responsive and dynamic :)

Also, because of this formula, I can then modify it slightly to use a parameter input for the desired length multiplier of the offset curve.  Here's my slightly modified formula...

Attachments:

• ellipse_offset.gh, 9 KB