Perfect Circle Made Out Of Quadratic Bezier Curves

Before asking a question on FontCreator look here for possible solutions and tutorials. Please do not post support requests here.
Post Reply
Erwin Denissen
Moderator
Moderator
Posts: 9330
Joined: Fri Oct 04, 2002 12:41 am
Location: Bilthoven, The Netherlands
Contact:

Perfect Circle Made Out Of Quadratic Bezier Curves

Post by Erwin Denissen »

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
ellipsedrawingtool.png (10.79 KiB) Viewed 12483 times
It contains 4 on curve points, and 8 off curve points as shown here:
basiccircle.png
basiccircle.png (3.29 KiB) Viewed 12483 times
The (almost) perfect circle contains 4 on curve points, and 16 off curve points as shown here:
perfectcircle.png
perfectcircle.png (7.93 KiB) Viewed 12493 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
comparedwithbasiccircle.png (7.51 KiB) Viewed 12493 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 380 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 351 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
High-Logic
Proven Font Technology
Bhikkhu Pesala
Top Typographer
Top Typographer
Posts: 9113
Joined: Tue Oct 29, 2002 5:28 am
Location: Seven Kings, London UK
Contact:

Re: Perfect Circle Made Out Of Quadratic Bezier Curves

Post by Bhikkhu Pesala »

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).
My FontsReviews: MainTypeFont CreatorHelpFC13 Pro + MT10.0 @ Win10 2004 build 19041.867
Dave Crosby
Typographer
Typographer
Posts: 793
Joined: Mon Feb 23, 2004 1:13 pm
Location: Enoch, Utah

Re: Perfect Circle Made Out Of Quadratic Bezier Curves

Post by Dave Crosby »

So much simpler and direct than my meanderings of long ago. Thanks Erwin!
Aut nunc aut nunquam
Post Reply