Re: Evaluation of interpolating-scheme (such as butterfly) at an arbitrary parameter value
In Reply to: Evaluation of interpolating-scheme (such as butterfly) at an arbitrary parameter value posted by Jianbing Huang on February 27, 2005 at 13:20:34:
: Is there any work on evaluating subdivision surfaces of an interpolating scheme such as butterfly at an arbitrary parameter value? I have seen papers addressing the evaluation issue on approximate schemes such as Catmull-Clark and Loop - is the method on approximating schems just a trivial extension or there exists extra difficulties? Thanks.
The method that you refer to is Stam's method for evaluating Catmull-Clark and Loop surfaces. In this case, he relies on the fact that an ordinary patch can be evaluated exactly using methods like blossoming away from extraordinary vertices. Unfortunately, for interpolatory schemes, there exists no such method for exact evaluation even away from extraordinary vertices at arbitrary parameter values. Joe Warren gave a talk at SGP last year that spoke a little about exact evaluation of the four-point curve subdivision scheme. However, even that talk fell short of a general purpose method for just a curve subdivision scheme.