## Motion curve offset

### Motion curve offset

I'm pretty new to dealing with motion curves etc in Layout so need some help
here...

I've created a long motion path for an object and would like to clone the
object 100's of times.

I'd then like to randomly offset the clones on that motion path so they
appear to be following each other down a road.  How would I best go about
this considering that the clones maybe running into the thousands?
Obviously some sort of quick or automatic approach would be best using a
plug-in maybe?

Any tips with the graph editor or plug-ins would be very helpful indeed.

Many thanks

Buzz

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

--
--------
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