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Access measure value of point on feature in featureLayer?

Question asked by chris.chalstrom on Apr 13, 2012
Latest reply on Nov 17, 2015 by

I have a feature layer set up in ArcMap 10.  This feature layer is composed of a set of polylines. 
I followed the steps at this URL:
to set up a route that has M values for each vertex in the polyline.  When I start editing -> double click a line -> click sketch properties, I can see that the M value has been correctly set for each vertex.

How can I access this information via the javascript API?  I have a feature layer set up with this feature layer added to it.  But when I click the feature layer, I can't get the measure information.  I can get the e.graphic.geometry and so on, but there isn't measure info associated with any of the points.

What would be even better is if I could get the exact measure value for a specific point on the line (a point that is not necessarily the same as any vertex which composes the line).  Is it possible to do this with the javascript API?  If so, how?