Below how you can achieve in REST API.
First you need to make call to your targeted view,
/sites/mysc/_api/Web/Lists(@v0)/Views(@v1)?&@v0=guid'4fc236a-4364-4523e-a523a-abd90e0e0583'&@v1=guid'f0e92334-6c47-4223-9d1a-6b7ea5d239ada'
Here above v0 should your list GUID and v1 should be your view guid.
Once you make call to above service, you will get CAML Query associated with this view.
it would be available in ViewQuery attribute. For e.g data.d.ViewQuery
I get below output for my query
ViewQuery: "<OrderBy><FieldRef Name="ID" /></OrderBy>"
Keep this query in some variable say 'caml'.
Next thing to do is call REST API based on above CAML Query. Here we would use Post method and pass 'data'. Ref link
var data = { "query" :{"__metadata": { "type": "SP.CamlQuery" }, "ViewXml": caml}};
Now if you are using ajax to make REST Call, call would be something like below.
$.ajax({
url: siteUrl+"/_api/web/lists/GetByTitle('"+ listName +"')/GetItems",
method: "POST",
data: data,
headers: {
"X-RequestDigest": $("#__REQUESTDIGEST").val(),
'content-type': 'application/json;odata=verbose',
'accept': 'application/json;odata=verbose'
}
success: function (response) {
///do your code
},
error: function (data) {
///do your code
}
});