Sliding an Edge or Vert w/o stretch/pinch texture image?

[Fonte Boa]

Not sure what exatcly you're intending to do,
but why dont you use an Image Plane (with the tree image as reference)
to build your geometry (outlining the tree with edges and verts)
and after this, just then, you UV map this geometry so that you can apply
the tree image as texture?

If you apply the texture before build the topology you need,
you will be distorting all the time the uvmapping already built...