Converting an Ellipse to a Polygon

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 and the 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:

1. Draw an ellipse, any size
2. Use the Point tool to insert a Point into the drawing (any location)
3. Select the point in (2) and choose Edit menu > Cut
4. Select the ellipse drawn in (1) and choose Edit menu > Objects on Path...
5. In the Objects On Path dialog, click the Clipboard^? radio button, click the Distribute radio button and enter the desired number of segments in the Objects field. For example, enter 12 to create a 12 sided polygon. Press OK
6. Result: the point from step (3) is inserted 12 times, equally spaced, around the perimeter of the ellipse
7. use the Polygon tool to connect the points created in step (6).
8. Result: you have a polygon that connects the points touching the perimeter of the ellipse but the segments are not of equal length
9. Select the polygon drawin in step (7) and choose Tool menu > Area to insert the perimeter of the polygon into the drawing
10. Select the numeric value of the perimeter inserted in step (9) and choose Edit menu > Copy
11. Draw a Line and press Tab to activate the edit window. Tab into the Length field and choose Edit menu > Paste. At the end of the data pasted, type the / symbol (divided by). Enter the number of sides you of the polygon. In our example, we'd enter 12. Press Enter
12. Result: the line drawn in step (11) is now exactly 1/12 the length of the perimeter of the polgon. Press Tab to activate the Edit Window and Copy the Length of the Line
13. Select the Polygon drawn in step (7) and choose Edit menu > Edit... to open the Polgon EditDialog
14. Click the Angle radio button and observe the Len: field (Length) is activated.
15. Select the contents of the Len: field in step (14) and choose Edit menu > Paste. Click the >> button to proceed to the next point and, again, select the contents of the Len: field and choose Paste. Repeat this step until you've pasted the correct length for every segment
16. Important you must do step (15) twice. That is, Paste the correct segment length into the Len: field for every segment Twice. This ensures that there aren't any incorrect segment lengths. Press Ok
17. Result: the polgon now has segments of equal length that touch the perimeter of the ellipse.

To confirm the result, you can select the final polgon and choose Tool 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

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.

1. choose the Ellipse tool and draw an Ellipse
2. press option and click on the Polygon, Regular tool
3. special 10 sides and click the by center to vertex radio button
4. use Center snap to draw the new polygon from the Center fo the ellipse
5. use Vertex snap to end the drawing operation for the polygon at the top most point of th ellipse
6. stretch the right most mid point control point of the polygon to match the right most point of the ellipse
7. repeat step (6) for the left side of the polygon

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

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:

1. choose the elliptical arc tool and draw one quadrant of the ellipse
2. choose the Point Tool and click to insert a single point anywhere in the drawing
3. select the point in (2) and choose Edit menu > Cut
4. select the arc in (1) and choose Tool menu > Objects On Path...
5. in the objects on path dialog box, click the Clipboard^? radio button, click the Distribute radio button and enter the desired number of items in the objects field. For example, if we want to draw 3 segments, insert 4 objects on the path
6. Press OK and the points are inserted on the path of the ellipse
7. choose the Line tool and draw lines to connect the dots
8. now simply select the line segments, and mirror them to create the rest of the shape

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

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

1. Select the Ellipse
2. choose Tool menu > Convert to Polygon
3. the ellipse is now a polygon

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 the Tool menu > Polygon submenu to further modify the geometry.