When I draw a perfect circle of about 100 units (in a 1000 units grid) and rotate it 45 degrees, it is no longer perfectly round. Can I create a circle that keeps its roundness while I rotate it? Do I therefor have to change the size of the circle or the size of the grid?
- a truly perfect circle is not possible in PostScript. So we are only taking about a good-enough approximation.
- The coordinates of on-curves and off-curves snap to the grid. You can set your subdivision to 10 or 100, and see if the result is acceptable to you. Or you can draw larger circles
Thanks. I couldn’t find a mathematical rule for creating a perfect postscript circle. Good to know that I can stop searching.
Experimenting with circles of different sizes (rotate 45 degrees, add extremes and rotate 45 degrees again) shows that some sizes work better than others. 96 units works quite well.
the closes you can get with four segments is to set the handle length to 56.6% of the segment height. Thats why I use 57% in the fit curve dialog as circles look better if they are slightly to square.
It depends on what your definition of the best approximation is.
According to http://www.tinaja.com/glib/ellipse4.pdf, if you want an exact fit at t=0.5 (half way through a segment), then 55.228475% is best. If you want an exact circle fit every 30 degrees, then 55.1784% is best.