Structure.Gantt REST API is under development. The functionality available through REST is sometimes not complete, but it allows you to work with the Gantt charts, Baselines, and Resource Leveling.
General Notes
REST Resource Addresses
Structure.Gantt REST API resources have the URL prefix
${BASEURL}/rest/structure-gantt/public/${VERSION}/{NAME}
where BASEURL is the base Jira address (http://localhost:2990/jira being the standard base URL for development environments), VERSION is the version of the API (currently only version 1.0 is available), and NAME is the name of the resource.
Authentication
Authentication is done via the standard Jira authentication engine and supported by cookies. When accessing REST API from a remote application, you may need to set up the session first by calling the Jira authentication REST resource. (You don't need to do that if you access Structure.Gantt REST API from a JavaScript on a page from the same Jira instance.)
Most read operations are available to non-authenticated access (subject to permission checks for the anonymous user). Most mutation operations are available to authenticated users only.