Perfect Circle Made Out Of Quadratic Bezier Curves

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Erwin Denissen
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Location: Bilthoven, The Netherlands

Perfect Circle Made Out Of Quadratic Bezier Curves

Post by Erwin Denissen » Fri Mar 18, 2016 1:49 pm

Since we regularly receive requests about a perfect circle made out of Bezier curves (and discussed this long ago), I've made a circle which is so close to perfect, that it is worth sharing.

FontCreator contains a basic ellipse drawing tool, which can also create a circle sufficient for most needs.
ellipsedrawingtool.png (10.79 KiB) Viewed 6553 times
It contains 4 on curve points, and 8 off curve points as shown here:
basiccircle.png (3.29 KiB) Viewed 6553 times
The (almost) perfect circle contains 4 on curve points, and 16 off curve points as shown here:
perfectcircle.png (7.93 KiB) Viewed 6563 times
Here is a quarter of the circle, along with a basic circle (made out of 4 on curve and 8 off curve points). The basic curve is the one on the right, as it is a bit too large in some places.
comparedwithbasiccircle.png (7.51 KiB) Viewed 6563 times
In general the basic circle is made out of fewer points, so is more compact. When used at small sizes it is good enough, but occasionally you might need a more perfect circle. Then feel free to use the one as available in the font project file "Circle Perfect Bezier":
Circle Perfect Bezier.fcp
(3.05 KiB) Downloaded 243 times
And the font file containing a circle for the ASCII character range can be downloaded from here:
Circle Perfect Bezier.otf
(6.05 KiB) Downloaded 223 times
In case you didn't know it, keep in mind you can't describe a perfect circle with bezier curves, but you can come close. Since font outlines are internally stored as integers (whole numbers), the rounding errors are inevitably affecting the actual position of the points.
Erwin Denissen
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Bhikkhu Pesala
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Re: Perfect Circle Made Out Of Quadratic Bezier Curves

Post by Bhikkhu Pesala » Tue Jun 28, 2016 5:29 pm

In FontCreator 10, a perfect circle (or ellipse) with 20 points is created automatically using the ellipse tool if the largest dimension is greater than the em square. That's 2048 funits for most fonts (see the General tab of the Font Properties dialogue to check).
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Dave Crosby
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Re: Perfect Circle Made Out Of Quadratic Bezier Curves

Post by Dave Crosby » Wed Jul 13, 2016 3:35 pm

So much simpler and direct than my meanderings of long ago. Thanks Erwin!
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