You can use the handy technique of "see how Workspace does it" to see how to format the segment GET request. As an example, I turned on Developer Tools in my browser, then created a new Workspace project, and I can see the call to the segment service go across the wire like so:
Request URL: https://appservice5-10.omniture.com/analytics/1.0/segments/?locale=en_US&includeType=shared,templates,curatedItem&dataType=oberon&curatedRsid=geo1metrixxgeometrixx.outdoors&expansion=favorite,approved,tags,usageSummaryWithRelevancyScore,modified,internal,compatibility&toBeUsedInRsid=geo1metrixxgeometrixx.outdoors&limit=10000
Although you will be making calls through the Adobe IO gateway and not to the raw Workspace endpoints, the API request/response format is the same. So to get the list of segments Workspace displays in the left rail, which are the segments you own as well as those that are shared with you, you need to supply the "includeType" parameter and set its value to "shared". You can also supply the "templates" value to retrieve any segment templates. You likely won't have use for the "curatedItem" value but it includes any segments that were curated along with the report suite specified in the curatedRSID parameter.
