Comparing a folder with a git repository's subfolder

You can recreate the directory structure leading to the subfolder and take advantage of the --relative option to commands such as diff and log (but not status). For example, if you have a checkout of sub/dir:

mkdir -p sub
mv now sub/dir
git --git-dir=/repository.git diff --relative=sub/dir

You can populate a temporary index file with just the contents of the subdirectory of the repository and then diff the existing files against it.

diff-sub() { : usage: diff-sub repo treeish-in-repo external-dir
  (
    GIT_DIR="$1" GIT_WORK_TREE="$3"
    GIT_INDEX_FILE=/tmp/.git-index--now-sub.tmp
    if test -e "$GIT_INDEX_FILE"; then
      echo "already exists: $GIT_INDEX_FILE"
      exit 1
    fi
    export GIT_DIR GIT_INDEX_FILE GIT_WORK_TREE
    git read-tree "$2" &&
    git diff
    ec=$?
    rm -f "$GIT_INDEX_FILE"
    exit "$ec"
  )
}
: diff sub from master in /repository.git against /now
diff-sub /repository.git master:sub /now

Note: If you run other Git commands that compare against the normal, full tree (e.g. git status or git diff --cached instead of git diff), then you will see odd-looking results since both the index and the working tree only contain a portion of the normal, full tree.