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 Edit Window to specify your desired Height and Width values (they don't have to be equal), then proceed directly to stage two. That saves you some steps and is the more likely procedure to be used during production. quicktime Click Here to see a Demonstration Movie (2.6MB Download) of the quick way to see just how easy it is! (need movie help?), Read on to see all the detailed, step by step instructions.

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

  1. Draw an ellipse with the general desired proportions
  2. Option click on the Polygon, Regular tool and specify 12 for the number of sides and click the by vertex icon. You could enter any number of sides you like but it's important to select the by vertex radio button since we're drawing one perfect quadrant of the polygon.
  3. use Center Snap to start drawing the polygon from the center of the ellipse.
  4. 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
  5. drag the mid point control handle bar and snap it to the right most end point of the ellipse

    6. 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

  1. select the polygon and choose Tool menu > Polygon > Distribute Points
  2. Use the Knife tool to break the polygon so you're only working on one quadrant of the ellipse.
  3. select the polygon and choose Edit menu and the Poly Edit... dialog will open
  4. Delete the extra point (point 5 in our example) by pressing Delete
  5. Click the AngleRadio button. Observe the length of each segment of the polygon is displayed
  6. Enter a value in the Length field and press the >> button to advance to the next segment
  7. Enter the same value for this segments length
  8. Repeat for each segment and press Ok
  9. 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, quicktime 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 Edit menu > Mirror to complete the entire shape which could then be Attached to create one contiguous polygon.

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
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