Using a projector and a couple of stacked boxes, I’d like to do 3D projection mapping:
The above video shows an animation. To keep things simple, all I need is a still image, i.e. I don’t need animation. I imagine placing texture maps on surfaces, and then use some tool to create a projection map based on the camera perspective.
Is this possible using Rhino or some of its plugins?
you should be able to do this with planar maps applied to the individual surfaces…
Indeed, I think simply applying planar maps to the boxes, then rendering the camera perspective should be all that’s needed. Seems like I missed the obvious - it’s very hot here today. 
The challenge is alignment. Naively I tried _PerspectiveMatch with a dummy wallpaper image covering the entire viewport, then I clicked on points in the projection, and on corresponding points in the model, but mapping didn’t work. Any other suggestions?
Could be that I need a 3rd party software…
No extra software needed, but you do need to know the position of the projector as well as the projector lens parameters.
When I do this through rhino I do the setup live with the projector connected to give tune the view.
A screencast showing me picking points in the projection. The seven numbered points visible near the end signify where the vertices of the box should be in the projection. Yet the perspective chosen by _PerspectiveMatch is totally off:
Am I doing something wrong, or is this a software bug?
Manual and automatic keystone correction is disabled in the projector. In the end I did the mapping with VPT, but that was tedious: