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# HE_Mesh challenge: transform smoothly from one mesh to another

I've been wondering how it might be possible, given two meshes, to find mutations that transition smoothly from one to the other. If both meshes are placed in relation to the same zero point on the X, Y, and Z axes, then it seems to me it would be possible to draw a line from the zero point to any vertex in one mesh, and then to find the closest line that goes from the zero point to a vertex in the other mesh. That vertex in the second mesh would serve as the target for the vertex in the first mesh, and this process of finding a 'twin' vertex would be carried out for all vertices. Would this be possible?

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• Possible, yes, but only for meshes that are "similar" enough for that to work.

Consider, say, the mesh of a simple cube turning into the mesh of a sphere. The cube has a lot less vertexes/faces than the sphere, so unless you somehow add additional mesh points, you're going to end up with a very poor-looking sphere. The issue here is that a difference in mesh point numbers can make meshes very not-similar.

Also imaging trying to turn a mesh of a sphere into the mesh of a torus. While you could do this by bringing the poles of the sphere to its center and then "expanding" them into hole, trying to do it using nearest-final-destination logic (as you've described) might be cumbersome, and not result in the desired end mesh at all!

It really depends on the meshes you're trying to start and end with. If you know what they are in advance, you might be able to do better. It's not a simple problem, and the generic solution might not be the best way.

Does that make some sense? I don't feel like I'm explaining this very well.

• I'm not trying to end up with a good-looking sphere. I'm more interested in the in between stages, so ending up with a poor looking sphere could be exactly what I'm after. Although, I'm not dealing with simple shapes - finding a fusion between two shapes is the whole point of the whole exercise (and by fusion I don't mean grafting part of one onto the other). As far as numbers of vertices are concerned, I had thought about that, but I believe it's possible in HE_Mesh to subdivide faces. But even if there are quite radically different numbers of vertices, that's not necessarily a problem. I'm just looking for that closest analogous vertex in the other mesh.

So if it's possible, how would it be done?