When and How to Convert AutoCAD Ellipses into Arcs

Designers Love swoopy ‘Organic’ Shapes. Unfortunately fabricators like defined geometry. Sometimes it falls to Us to convert one to another.

We’ve all been in that situation ;) Our Boss thinks we can use the Designer’s file as it is, but we know that the CNC machine won’t take the geometry. If you are in this situation, there are a few AutoCAD tricks you can use to convert an Ellipse (or any Spline) into Polylines. However, sometimes the best method is to redraw the offending geometry yourself. That is when these old tips from the drawing board really come in useful.

What is an Ellipse?

An ellipse is the locus of all points of the plane whose distances to two fixed points add to the same constant.

The distance from F1 to PTn to F2 is always equal to the Major diameter   a to -a

Points F1 and F2 are called the Focus points (or Foci).

A definition of an An Ellipse

You can find the Focus points of an Ellipse by drawing and Arc equal to the Major radius O to a from the end point of the Minor radius b. The Focus points are where the Arc crosses the Major Axis

Finding the Focii of an Ellipse

Ellipses for CNC

Ellipses can easily be drawn with AutoCAD’s ‘ELLIPSE’ Tool. However, most CNC machines won’t accept ellipses.

Your CNC Programmer may be able to convert AutoCAD ellipses to Polylines using a program such as Alphacam – but if it falls to you to provide an elliptical Polyline then there are a number of simple techniques you can use.

A comparison of Ellipse Conversions with AutoCAD

a. This is the original Ellipse.

b. Firstly, you can set the Autocad variable ‘PELLIPSE’ to 1 (just type ‘PELLIPSE’ at the command line and follow the prompts). This will instruct Autocad to draw all Ellipses as polyline approximations (My preferred option).

c. If you offset an Ellipse, you get a spline (this makes sense, from a geometry point of view, All points on the curve are no longer equidistant from the Foci). You can offset the original ellipse,  delete the original Ellipse and then offset the spline back by the same amount to create a spline version of the Ellipse. Of course we want a polyline – not a spline so we have another process to go through.

d. You can use the Autocad Express tool ‘FLATTEN’ to convert a Spline into a Polyline.

or

e. You can use Autocad 2010’s new ‘SPLINEDIT’ command to convert a spline to a polyline.

f. Finally – if you don’t have Autocad 2010 or you don’t have the express tools loaded you can use the ‘DXFOUT’ command to export the Ellipse to an Autocad R12 DXF. Ellipses weren’t supported in R12, so the Ellipse will be converted into a Polyline.

There are also various 3rd party programmes available to convert Ellipses and Splines to Polylines, but I won’t cover those here.

As you can see, the Ellipses are converted with various degrees of complexity. My preferred choice is to simply re draw the Ellipse with ‘PELLIPSE’ set to 1.

Ellipses for Tube Rolling

The techniques I’ve described might help you with CNC machined parts, but what if you are drawing up a an Elliptical metal frame? Tube and Pipe rolling machines typically only roll one radius at a time, and each radius will need to be welded together to form the Ellipse. The Polylines I’ve shown above have too many Arcs for this purpose. Our best option may be to re-draw the Ellipse using the same techniques we would have used on the drawing board.

There are a number of different techniques available for drawing Ellipses with Arcs. I will demonstrate two of them here.

Four Centre Ellipse

To set out a four centred ellipse:

  • Draw out the Major and Minor axis
  • Draw a line from a to b
  • Mark off the point d. The distance b to d = OaOb (i.e. The difference between the Major and Minor Radii)
  • Draw a perpendicular line to bisect Line d to a
  • Where this new  line e meets the extension of  Axis b you will find the first centre point C1
  • Where line e cross Axis a you will find the second centre point C2
  • Line e also marks the point where the two arcs meet
  • You can mirror the geometry around the Axis to find the remaining centre points and complete the Ellipse.

Setting out A Four Centred Ellipse

…If this Four centred Ellipse isn’t accurate enough…

Five Centre Ellipse

To set out a five centred Ellipse:

  • Mark out the Major and Minor Axis
  • Draw a line a to d and d to b
  • Draw a line a to b
  • Draw a line perpendicular to ab through point d
  • Where this new  line d meets the extension of  Axis b you will find the first centre point C1
  • Where line d cross Axis a you will find the second centre point C2
  • r is the distance from C2 to a
  • Mark a point e two times the length of r from b on the minor Axis
  • Draw an arc with the centre at C1 and a radius of C1 to e
  • Draw an Arc with the centre at C2 and a radius of r
  • Where the two arcs cross you will find C3
  • Draw a line through C1 and C3 to find the meeting point for arcs A1 and A2
  • Draw a line through C2 and C3 to find the meeting points of arcs A2 and A3
  • You can mirror the geometry around the Axis to find the remaining centre points and complete the Ellipse.

Setting out a Five Point Ellipse

A comparison of Ellipses

Neither of these techniques will give you a ‘perfect’ Ellipse, but the difference will be undetectable to the naked eye.

A Comparison of AutoCAD conversions and hand drawn Ellipses

Looking for more CAD/CAM/CNC tips & tricks? Check out this post on cleaning up your AutoCAD DWG files for CNC.

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Comments

  1. chad says

    one note on your last section– I’ve used the four-centered approach for a project, and while the difference is fairly minor, it becomes more apparent the longer your ellipse is– ie, the less it is like a circle. Handy to keep in mind while picking a method.