Getting the parent of a directory in Bash

If I have a file path such as...

/home/smith/Desktop/Test
/home/smith/Desktop/Test/

How do I change the string so it will be the parent directory?

e.g.

/home/smith/Desktop
/home/smith/Desktop/

Solution 1:

dir=/home/smith/Desktop/Test
parentdir="$(dirname "$dir")"

Works if there is a trailing slash, too.

Solution 2:

Clearly the parent directory is given by simply appending the dot-dot filename:

/home/smith/Desktop/Test/..     # unresolved path

But you must want the resolved path (an absolute path without any dot-dot path components):

/home/smith/Desktop             # resolved path

The problem with the top answers that use dirname, is that they don't work when you enter a path with dot-dots:

$ dir=~/Library/../Desktop/../..
$ parentdir="$(dirname "$dir")"
$ echo $parentdir
/Users/username/Library/../Desktop/..   # not fully resolved

This is more powerful:

dir=/home/smith/Desktop/Test
parentdir=$(builtin cd $dir; pwd)

You can feed it /home/smith/Desktop/Test/.., but also more complex paths like:

$ dir=~/Library/../Desktop/../..
$ parentdir=$(builtin cd $dir; pwd)
$ echo $parentdir
/Users                                  # the fully resolved path!
 

NOTE: use of builtin ensures no user defined function variant of cd is called, but rather the default utility form which has no output.