Q:

How to use BezierCurve or BSplineCurve to define a quarter of a circle?

I know the command Circle can do that too, however, I want to be more flexible later on and want to know how to define this with the above mentioned functions. Thanks in advance!

A:

This will give a quarter of a circle,
Graphics[BSplineCurve[{{1, 0}, {1, 1}, {0, 1}},
  SplineWeights -> {1, Sqrt[2]/2, 1},
  SplineKnots -> {0, 0, 0, 1, 1, 2}]
 ]

and this gives the whole circle,
Graphics[BSplineCurve[{{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 
    0}, {-1, -1}, {0, -1}, {1, -1}, {1, 0}},
  SplineWeights -> {1, Sqrt[2]/2, 1, Sqrt[2]/2, 1, Sqrt[2]/2, 1, 
    Sqrt[2]/2, 1},
  SplineKnots -> {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 4}]]

I got the info to make these from a combination of this page and this page.  This page looks very useful for digging into the theory behind it all.

