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non-stationary scheme for circle construction

Posted by hjb_zy on March 16, 2005 at 22:51:45:

I am looking for a subdivision method to reproduce a circle. The paper "A subdivision scheme for Surfaces of Revolution" does provide a method that incorportes a tension factor that changes its value from one level to the next. However, it seems that for the proposed approach there is one important question that remains unanswered. What is the radius of the circle produced by a square of length 2? Or how to decide the length of the square in order to produce a circle with unit length (I have got a magic number 1.1107202 at float point precision by trial and error)? There does not seem to be a straightforward answer here due to the inherent complexity of the non-stationary scheme. Am I missing anything here? Do you have any suggestions to my problem - I am looking for a subdivision rule that can create a circle of a given radius from a cube with very high precision (the radius can be very large or very small). One alternative could be "A recursive subdivision scheme algorithm for piecewise circular spline" by Sasri published at Computer Graphics Forum
Volume 20, Issue 1 (2001)? Your opinion is highly appreciated. Thanks.

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