garageCube

I would like to map photos onto odd shapes without distorting the photos. Conceptually, the image being mapped would float freely independent of the quad so that regardless of the quad's shape, the image itself reflects its original perspective (although you may only see part of the image). For instance, in the example screenshot, the text becomes stretched as it fits to the pulled out corner of the rectangle. I'm sure I'm just not setting this up correctly, but am getting nowhere so thought I'd ask. Thanks for any and all help.

You can do it by activating Mesh Warping and enable the "show input mesh" option and the "link input-output" option, then you can move handles in the uv preview and handles in the output preview will follow, so no distortion.

OK. I activated Mesh Warping and I enabled Show Input Mesh and Link Input-Output. But, I still seem to be quite distorted and unable to remove the distortion. As an example, in this screenshot I'm shooting for the word "Photoplay" to be horizontal. I purposefully made the quad super angular so that the problem is clear. Again, thanks.

Success! I should have been using a mask - add the undistorted quad, then an inverted mask, voila! Thanks for your patience.