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Re: non-stationary scheme for circle construction

Posted by hjb_zy on March 22, 2005 at 11:03:28:

In Reply to: Re: non-stationary scheme for circle construction posted by Scott Schaefer on March 21, 2005 at 12:54:17:

: : 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.

: My master's thesis built a non-stationary, interpolatory scheme for surfaces of revolution that generalizes the four-point rule. This scheme is similar to the method presented in "A subdivision scheme for Surfaces of Revolution" except that it is interpolatory. Since the scheme is interpolatory, you know exactly what the radius of the circle will be when you construct the shape. The thesis is entitled "A Factored, Interpolatory Subdivision Scheme for Surfaces of Revolution". I can send you a digital copy if you would like.

Yes, I would appreciate if you can send me a digital copy of your master thesis. The accurate fitting of circular shape is very important in CAD.

The broader subject of fitting a subdivision surface to a general NURBS representation seems to be a hard problem also. While the sharing of the control vertices is the advantage of subdivision surface, it does seem to introduce additional difficulty in the fitting due to the size of the global matrix we have to deal with. There are also some works that use iterative local fitting - for example the work by Suzuki and the quasi-interplation method by Nathan Litke. Can you also provide some insight here - it seems that with the special rules for sharp edges local fitting is a better method anyway?

Thanks a lot.

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: : : 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. : : My master's thesis built a non-stationary, interpolatory scheme for surfaces of revolution that generalizes the four-point rule. This scheme is similar to the method presented in "A subdivision scheme for Surfaces of Revolution" except that it is interpolatory. Since the scheme is interpolatory, you know exactly what the radius of the circle will be when you construct the shape. The thesis is entitled "A Factored, Interpolatory Subdivision Scheme for Surfaces of Revolution". I can send you a digital copy if you would like. : Yes, I would appreciate if you can send me a digital copy of your master thesis. The accurate fitting of circular shape is very important in CAD. : The broader subject of fitting a subdivision surface to a general NURBS representation seems to be a hard problem also. While the sharing of the control vertices is the advantage of subdivision surface, it does seem to introduce additional difficulty in the fitting due to the size of the global matrix we have to deal with. There are also some works that use iterative local fitting - for example the work by Suzuki and the quasi-interplation method by Nathan Litke. Can you also provide some insight here - it seems that with the special rules for sharp edges local fitting is a better method anyway? : Thanks a lot.

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