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How to filter an object based on a filter object

Is there a convenient way to filter bigObject with only the properties defined in filterInterface to get filteredObject as output?

The big object has a lot of properties and I want to strip the information down to the properties I need (to save it somewhere, don't want to/can't save the complete object).

I prepared the following code as a jsfiddle here.

// My big object
var bigObject = {
    prop1: {
        prop2: {
            prop3: 123,
            prop4: 456,
            prop5: "TEST"            
        },
        prop6: 789,
        prop7: "xxx"
    },
    prop8: 5.6,
    prop9: 3    
}; 

// My "interface" to filter the object
var filterInterface = {
    prop1: {
        prop2: {
            prop3: true,
        },
        prop7: true
    }                
};

// My expected result, only the properties of 
// big Object which match the interface
var filteredObject = {
    prop1: {
        prop2: {
            prop3: 123,
        },
        prop7: "xxx"
    }                
};

Briefly, I'd expect something like:

var filteredObject = {}

for (var key in filterObject) {
  if (bigObject.hasOwnProperty(key)) {
    filteredObject[key] = bigObject[key];
  }
}

Include recursion if you want "deep" filtering:

function filter(obj, filterObj) {
  var newObj = {};

  for (var key in filterObj) {

    if (obj.hasOwnProperty(key)) {

      if (typeof obj[key] == 'object' && typeof filterObj[key] == 'object') {
        newObj[key] = filter(obj[key], filterObj[key]);

      } else {
        newObj[key] = obj[key];
      }
    }
  }
  return newObj;
}


var o = filter(bigObject, filterInterface);

alert(o.prop1.prop7); // 'xxx'
alert(o.prop1.prop9); // undefined

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