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Thread Subject:
morphing 2d curves under special conditions

Subject: morphing 2d curves under special conditions

From: Johannes Korsawe

Date: 19 Apr, 2011 14:09:20

Message: 1 of 1

Dear community,

i have the following task to fulfill:

Consider two curves c1 and c2 with size(c1) = [n1 2], size(c2) = [n2 2] with different total lengths (say c2 is shorter than c1), but "nearly" parallel, each without knots or self intersection, nice and smooth (ok, lets say, they are also not degenerated in the sense, one could see those two as real function graphs over some (differing) range of x (can be rotated to fulfill this condition)).

I want to morph one into the other under the following conditions:

1. As the total lengths are different, the "last" morphed line does not equal c2, but does contain c2.
2. Possibly, the following applies: one of the endpoints of the morphed line has to coincede with one of the endpoints of c2.
3. All morphed lines in between have to have the same distance from each other IF c1 and c2 are parallel.
4. All morphed lines in between have to have "nearly" the same distance from each other IF c1 and c2 are "nearly" parallel.

The term "nearly" in (4.) means that the range of distances between two morphed lines should be minimal or at least tightly limited under all possible choices.

I already know the submission
http://www.mathworks.com/matlabcentral/fileexchange/27873-parallel-curves
and it could possibly serve as a starting point for the considerations.

I have a very complex approach of generating streamlines and a field of a vector valued function in between, but due to speed considerations i would rather use some geometrical approach (and it is also not really stable nor elegant).

You have any ideas out there?

Best regards,
Johannes

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