Unvisualize Parsons code

CJam, 21 bytes

qN/:.e>(o2%:i"DRXU"f=

Fold the lines (:) by vectorizing (.) a character-wise maximum operation e>. Since there is only one non-space character in each column, this one will be the result, as space has a smaller ASCII code than all printable non-space characters.

Unshift and print the first asterisk (o, then map every other (2%) remaining char to UDR using modular indexing.

Old solution (29 bytes)

'*qN/z2%'*f#0+2ew);::-"RDU"f=

qN/ gets input lines. z transposes this character matrix. 2% drops every odd row. '*f# finds the index of the asterisk in each row. 0+2ew); gets all successive pairs of indices. ::- computes their differences, and "RDU"f= maps them to letters (via modular indexing: 0 → R, 2 → U, -2 ≡ 1 → D). The leading '* prepends the asterisk.

EDIT: I changed 2ew to 0+2ew); to work around CJam not handling ew (successive slices) on lists that are too short. This makes the code work for the input string *.

Try it here, or watch it in action:

Pyth - 28 25 27 25 bytes

2 byes saved thanks to @Jakube.

s+\*@L"RDU"-VFtBxR\*%2C.z

Try it online here.

Python 3, 129 108 98 86 bytes

There are probably several ways to golf this, but I rather like that I got it all down to one line.

Edit: Now using ''.translate()

Edit: With many thanks to wnnmaw.

Edit: I changed the input format to an array of strings instead of a newline-separated string to save bytes. Also, in the last edit, I mixed up U and R, so I fixed that.

lambda a:'*'+"".join(('UR'[j<'/']+'D')[j>'/']for l in zip(*a)for j in l if j in'-/\\')

Input must be an array of strings. For the example above, this looks something like:

["      *-*                    ","     /   \                   ","    *     *                  ","   /       \                 ","*-*         *         *-*    ","             \       /   \   ","              *     *     *-*","               \   /         ","                *-*          "]

Ungolfed:

def f(a):
    s = ''
    for c in zip(*a):           # transpose
        for d in c:             # for each letter in column c
            if e in "-/\\":     # if that letter is either -,/,\
                if e < '/':     # if < '/' (same as if == '-')
                    s += "R"
                elif e > '/':   # if > '/' (same as if == '\')
                    s += "D"
                else:           # if == '/'
                    s += "U"
        return "*" + s          # in the code we ''.join() it all together
                                # in this ungolfing, we add to an empty string