You are Odysseus, and are finally free from Calypso (who has kept you captive for many years) after you drugged her while she was sleeping1. You wish to return to your homeland of Ithaca, but the ship you've stolen is a bit damaged and cannot steer. However, you have also stolen a map which contains the location of Calypso’s island as well as the locations of Ithaca and the small islands that lie in between, as well as information about the wind currents of the area. Your ship can only sail by the wind currents, but you get to choose the direction you start in (north, south, east, west). If the currents bring you to another island, you also get to choose the direction in which you depart that island.
Can you get home to Ithaca?
 Because that definitely happens in the epic.
The input consists of:
- positive integers w and h
- a w-by-h grid of characters representing the map, where:
~denotes calm sea
^denotes a wind blowing north
vdenotes a wind blowing south
<denotes a wind blowing west
>denotes a wind blowing east
cdenotes Calypso's island, your starting point
idenotes Ithaca, the destination
*denotes an intermediate island
Each “wind” character moves you one cell in the direction of the wind, and winds never form loops (i.e. there is no way to get trapped in a cycle of winds).
You may take input however you want (reading a file, from STDIN, as function parameters etc.)
Output a truthy value if it is possible to get to Ithaca, and a falsy value if that is not possible.
w=10, h=5 ~^~~~~~~~~ ~c>>*>>v~~ ~v~~v~~v~~ ~>>*<~~*>i ~~~v~~~~~~ Expected Output: True Explanation: Go east, then east again, then east again
w=8, h=5 ~~~~~~~~ ~~>>v~~~ <<c~~~~~ ~~>~i~~~ ~~~~~~~~ Expected Output: False Explanation: There are two paths that lead to cells neighboring Ithaca, but there is no wind on those cells.
w=5, h=2 <c>>> ~v~~i Expected Output: False Explanation: Although you can get to a distance of one cell away from Ithaca, the wind on that cell is eastward which pushes Odysseus off the map instead of to Ithaca.
w=20, h=6 ~~~~~~~~~~~~~~~~~~~~ ~~v<<<<<<*<<>>>v>~~~ ~~i~<<*<<<<c~~~*~~~~ ~~~~~~^~~~~v~~~^~~~~ ~~~~~~<<*>>>>>>^~~~~ ~~~~~~~~~~~~~~~~~~~~ Expected Output: True Explanation: North, then West
w=20, h=6 ~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~*<<>>>v>~~~ ~~i<v<*<<<<c~~~*~~~~ ~~~~v~^~~~~v~~~^~~~~ ~~~~v~<<*>>>>>>^~~~~ ~~~~v~~~~~~~~~~~~~~~ Expected Output: False Explanation: Although there is a wind leading to Ithaca, it is inaccessible.
Standard loopholes are prohibited. This is code-golf, so the shortest solution in bytes in each language wins.