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Place UV island back to it's original 3D location


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Is there any way to transfer back 2D UV islands back to their original 3D spaces?
The goal is to place 2D UV islands into the 3D model with matching orientation.

I tried to use bounding boxes to calculate the transform matrixes of each 3D part and transfer the island that way. I had many issues with that approach. After I tried to invert the matrixes turns out that each box define 'up' differently (Sometimes the model is upside down after the transformation, sometimes flipped etc.). I'm not sure if am I right, but looks like bounding boxes only care about the transformation of itself. Because once I transformed the 2D island to its place this way, the fit perfectly to the box, but the yaw was always off. The final problem is connected to the previous one. When an island is on the other side of the model (aka. needs to be rotated) the transformation ignores that.

My next attempt was to calculate the averages of the normals on each 3D piece and use that as a Y axis, to calculate the X and Z based on that. This approach was even worse because my coordinate system was sensitive to rotation.

I attached a demonstration video, of what my goal is (It does not need to be animated I only do this to demonstrate the goal)

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Not exactly that, but something similar. Wha t I need is to keep the islands flat, and only apply the orientation of the 3D version, then transform them to the center of the mass which I calculate for each 3D piece. I attached an example of what my goal is, and my previous attempt. The pighead might not be the best example because, the UV islande are rotated, in the optimal case all islands should have the same general direction

uv_to_right_place.hipnc

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