I am using the cloth simulator to create an a triangular flag. Everythig works fine, but now I have been asked to put a in image on this flag. So I add the image as plane, it creates a rectangular plane, however when changing this to a triangle, it screws the image. I would like just to cut the parts of the image that do not belong to the triangle, without deforming the image.
Load your image in a UV/image editor window, set the 3D viewport in a position that views the triangle from the top, go to edit mode, select all vertices, U to Unwrap and choose "project from view". Then, in the UV/image editor window you can Grab, Rotate, scale the UV map to fit exactly the part of the image you want in your flag. At the end of the process you will have to assign this image to the flag material as an image texture.
You have to use the UV/image editor to do that.
Image as plane loads the image, creates a rectangular shape and defines the UV map of this plane.
The UV map is the correspondence between the 3D view object vertices and the same vertices projected on an image (or texture).
So, first open a new view, set it to 'UV/Image editor' (1) and choose your flag image in it:
Now if not already done, make your flag look as a triangle in the 3D View in edit mode, select all the vertices in the 3D View, then (still in edit mode), move the vertices in the UV map view to adjust their positions as you want:
All I did was texture the triangular flag and instead of using UV mapping, selected Generate. Scaled it to suit with the sliders in the Mapping tab. The texturing wasn't shown in the gif from your bent pole question because it sent the gif to 9 MB !
The flag -
If when scaling, bits of the repeat images appear near the edges, take the image into Gimp and expand the canvas out so there is plenty of vacant space (bkd or aplpha layer) around the object pictured.