(Yesterday, 16:45)Manfred Schaefer Wrote: I need a circular segment from 22.5° to 45°.As Réné already explained, there is more to it than just rotation. You also have mirroring and scaling. Mirroring inverts the rotation from ccw to cw as you figured out.
If I understand your explanation correctly, I would end up with a segment from 45° to 67.5°.
This means I would have to reflect a circular segment from 0° to 22.5° across the x-axis and then rotate it by 45° about the y-axis. However, a rotation of 45° implies a factor of 0.707... which results in too many decimal places.
Yes, if the scaling is 1.00, then the entry in the rotation matrix is sin(45°)=cos(45°)=0.7071, which is less than 5 decimals. However, most of the time, the scaling isn't 1.00, but something else. In those cases, you would round or truncate it to 5 decimals.
Now comes the hard part. While the scaling in one unique use case may be such that the entry in the rotation matrix is more accurate for a 22.5° rotation, you always have to remember that there are two entries in the rotation matrix; a*sin(x) and a*cos(x). Usually, when sin(x)=cos(x), i.e. x=45°, you end up with less distinct entries in the rotation matrix. This makes it easier to combine multiple rotated primitives without introducing unnecessary microgaps.