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I want to sample DEM data, 30m resolution, at every 3m under a drawn line and wondering if there is any built-in tool within ArcGIS 10.1. My take on this is to convert line (feature) to point and somehow define point interval to be 3m and then retrieve elevation values for each of those points. Please suggest on how to control the point interval or any other way of handling this task.

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Try this: Use the Create Random Points tool to create your points at 3m intervals. Set your line feature as a constraining feature. Set the minimum allowed distance to 3m. Use the point interval and the length of the line to work out the number of points

You then use the Extract Multi Values to Points to get elevations values from the DEM.

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