Hi @Anonymous
I think I have a better understanding of what your looking for. You would like the morpher tool to also change the UVW to match the morph target. I don't believe there's a way to have the UV's morph at the same time as the mesh with the morpher tool alone.
So I tested a few things. I first tested to see if you could get the desired results with keyframing the texture map itself...which is possible, but would require a lot of finesse. You would need to apply the UVW, then the morpher modifiers, and animate the UVW map by memory, which isn't ideal.
A colleague also suggested using a camera map modifier to project the texture, but I haven't figured out how to get this to work, it still stretches with the geometry currently, I will keep you updated on if we figure out another workflow for this.
I hope some of this is helpful! I will talk to you soon.
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