# Converting an Ellipse to a Polygon

### Question

**How do I draw a polygon with segments of equal length that follow the shape of an ellipse?**

### Requirements

PowerCADD, any version

PowerCADD version 7.0.1 and Mac OS^{?} X Tiger 10.4.5 or newer recommended

### Background

There isn't any single, one step, method or tool to create the geometry you're describing. However PowerCADD does provide various simple techniques that can be combined to create the geometry you're describing.

### What To Do

Here's one way to create the geometry you're describing that looks like this:

We've elected to draw the ellipse first, as shown in the screen shot and as illustrated in stage one below for general reference. **However, it's important to note you do not need to draw the ellipse first!** You could simply draw the multi-sided polygon and use the

**To create an elliptical polygon with segments of equal length, do this:**

Stage One: Draw a multi-sided polygon that matches the shape of an ellipse

- Draw an ellipse with the general desired proportions
Option click on thePolygon, Regular tool and specify12 for the number of sides and click theby vertex icon. You could enter any number of sides you like but it's important to select theby vertex radio button since we're drawing one perfect quadrant of the polygon.- use
Center Snap to start drawing the polygon from the center of the ellipse. - use
Vertex Snap or End Snap to complete drawing the polygon along the Y axis. In effect the height of the new polygon matches the height of the ellipse - drag the mid point control handle bar and snap it to the right most end point of the ellipse

repeat step 5 for the left hand mid point. The result is a polygon that now matches the width and height of the ellipse. Notice the polygon segments are not of equal length

Stage Two: Set the polygon segments to the desired length

- select the polygon and choose
Tool menu > Polygon > Distribute Points - Use the
Knife tool to break the polygon so you're only working on one quadrant of the ellipse. - select the polygon and choose
Edit menu and thePoly Edit... dialog will open - Delete the extra point (point 5 in our example) by pressing
Delete - Click the
Angle Radio button. Observe the length of each segment of the polygon is displayed - Enter a value in the
Length field and press the>> button to advance to the next segment - Enter the same value for this segments length
- Repeat for each segment and press
Ok - Observe: the result as shown in the earlier screen shot.

**Wow!** that sure is a lot of steps and it's probably pretty hard to follow. Not to worry, Click Here to see a Demonstration Movie (2.7MB Download) of those steps and you'll realize just how fast and easy it is to do! (need movie help?)

In our example we added a few objects such as center lines to make it clearer and we've worked in millimetres to 12 decimal points of accuracy to illustrate how accurate this technique can be. We've also dimensioned the segments and used

Clearly the dimensions we selected for the segment lengths are arbitrary and you may need to be more precise in selecting your segment lengths to suite your particular drawing circumstances.

We hope that helps

*caddpower.com*

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## The Definitive Method

PowerCADD Canada was kind enough to point out that the definitive method is simple and is a combination of some of the methods we've described here.

In this method, the segments of the polygon are all of equal length

andthe vertices of the polygon touch/match the perimeter of the original ellipse. Again, the method will work with any version of PowerCADD. Here's what the result looks like:To draw a polygon whose segments are of equal length which touch the profile of an ellipse, do this:

^{?}Importantyou must do step (15) twice. That is,Twice. This ensures that there aren't any incorrect segment lengths. PressTo confirm the result, you can select the final polgon and chooseTool menu > Area to insert the Perimeter of the edited polgon.

This may seem like a lot of steps but again, it is much faster to do than it is to read and write. Click Here to see a Demonstration Movie (5.2MB Download) of the above stages and steps (need movie help?).

In the demonstration movie we've created a 12 sided polgon. To illustrate the degree of accuracy we've worked to five decimal points in millimetres (that 1/1000 of a millimetre accuracy). In our final result we've dimensioned polygon segments to five decimal points of accuracy in millimetres and you'll note the dimensiosn all match. You will also observer that our original polgon had a perimeter of 118.28942 millimetres. The final, edited, polygon has a peirmeter of 118.28939 millimetres. That a difference of 0.00003 mm or 3/1000th of a millimeter difference in the two perimeters.

We're not familar with any building contractor, site contractor, or other manufacturer that can create a product to 3/1000 of a MILLIMETRE accuracy so it seems that for all practical purposes, the above technique is accurate for real world purposes

## One more quick and dirty method

here's one more quick and dirty method to make a polygon that matches the profile of an ellipse

in this example we'll just make a 10 sided polygon that fits the X and Y (height and width) of an existing ellipse in the drawing.

CenterVertexClick Here to see a Demonstration Movie (1MB Download) of the above stages and steps (need movie help?)

## Another Method...

if you don't need the segments to be of equal length, there's another, very fast, option

To draw the segments of a polygon that fits the profile of an ellipse, whose segments are different lengths, do this:

^{?}Click Here to see a Demonstration Movie (2.0MB Download) of the above stages and steps (need movie help?)

## To simply convert an ellipse to a polygon

I should have also pointed out that if all you need is an ellipse simply converted to a polygon, just:

But be careful, an ellipse is what we refer to as a piece of high level geometry. That is, once you make a polygon out of it, you can't convert it back to an ellipse.

However, once the ellipse is converted (and there are multiple levels of conversion accuracy available when making the polygon), you can use the various options available in theTool menu > Polygon submenu to further modify the geometry.