Everyone knows how to draw a circle or a square. An oval is just an elongated circle just as a rectangle is an elongated square. A diamond is also straightforward to draw. These shapes, along with many others are tied together in what I call the theory of super circles. This Instructable will show just how to do it.
Step 1: X Radius, Y Radius, and Poly Order
A super circle is defined by its parmeters; X radius, Y radius, and Polynomial order. Don't let the name scare you, the Poly Order is a number that tells you how puffy the circle is.
To start. go to PolyDraw and set the # of Polys window to "1". You will get a screen with a single poly with; an X Radius of 4, a Y Radius of 4, and a Poly Order of 2" . Click Draw and you will get a PDF with a circle have a diameter of 8" (4" radius).
Now change the Y Radius value to 5 and hit draw. You now have a oval.
Change the Poly Order to 1 the new PDF will have a diamond.
Change the Poly Order to 100 and you will get something really close to a rectangle. (the Poly Order would have to be infinite for an actual rectangle.
Step 2: Draw a Specific Shaped Poly (Super Circle)
A Poly will have an X Radius, a Y Radius, and a D (diagonal) Radius. Unfortunately PloyDraw requires a Poly Order Value. The following program converts Poly Order to D radius or the reverse.
Suppose you want a Poly with an X radius of 4", a Y radius of 4", and a D radius of 4.25" . Enter these values into PolyAnalyze and solve for the Poly Order. In this case it is 2.424.
Enter these values into PolyDraw and you get a PDF of this Poly. Print it out and measure it to show it has a diagonal diameter of 8.5". Polys with a Poly Order around 2.3 to 2.6 have a very Asian feel to them. Less than 2.3 an it looks mostly like a circle. Above 2.6 and they have a squarish feel to them.
PolyDraw allows you to draw several Polys at a time. The photo at the start had 9.
You are now ready to draw super circles. There are also tutorials available that will help you learn to exploit more PolyDraw features.