1. Cubic Bezier curves: offsets, splitting, length?

I'm looking for solutions or at least good references on the following

problems concerning cubic Bezier curves in two dimensions:

1) Finding an offset curve, at a given distance, from a piecewise

cubic Bezier. (I realize the components of the offset won't have a

1-1 correspondence with the components of the original curve, but

that's not a problem for me.) Ultimately, I have to be able to

generate the offset without internal loops, etc.

2) Find the intersection of a Bezier and an upright rectangle. I am

currently doing this by polygonizing the Bezier and testing each

edge, but I thought there might be a faster way by doing it

directly.

3) Finding the length of a Bezier.

4) Finding the closest point on a Bezier to a given point.

5) Splitting a Bezier into two curves at some point.

Any recommendations, references, working code, etc. will be *greatly*

appreciated. I have some papers from years ago, but some of these are

too abstruse for me, and there may be newer information out there.

I've checked the Graphics Gems series, but it doesn't offer any

solutions for most of the above problems, and they're getting pretty

old now also.

Thanks very much,

-pd

--

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Peter Davis

Funny stuff at http://www.pfdstudio.com

The artwork formerly shown as prints

List of resources for children's writers and illustrators at:

http://www.pfdstudio.com/cwrl.html

2. ftp.gwu.edu back up

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