Averaging vector images to get in-between images

I am looking for an algorithm that takes vector image data (e.g. sets of edges) and interpolate another set of edges which is the "average" of the two (or more) sets.

To put it in another way, it is just like Adobe Flash where you "tween" two vector images and the soft开发者_如何学Cware automatically computes the in-between images. Therefore you only specify the starting image and end image, then Flash takes care of all the in-between images.

Is there any established algorithm to do this? Especially in cases like different number of edges?

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What exactly do you mean by edges? Are we talking about smooth vector graphics that use curves?

Well a basic strategy would be to simply do a linear interpolation on the points and directions of your control polygon.

Basically you could simply take two corresponding points (one of each curve/vector form) and interpolate them with:

x(t) = (1-t)*p₁ + t*p₂ with t in [0,1]

(t=0.5 would then of course give you the average between the two)

Since vector graphics usually use curves you'd need to do the same with the direction vector of each control point to get the direction vector of the averaged curve.

One big problem though is to match the right points of each control polygon, especially if both curves have a different degree. You could try doing a degree elevation on one to match the degree of the other and then one by one assign them to each other and interpolate.

Maybe that helps...