The only method I can think of is if you are using solid elements. The technique would work as follows:
For a simple case, lets say you have just 1 solid quad element. Any coordinate inside that element is some distance away from the 4 nodes. The farthest it could be from one of the nodes is from 1 corner to the complete opposite corner (call this distance 'd'). So to specify if a random coordinate is inside the element you would search through your list of nodes and determine how many nodes it finds that meet the criteria (magnitude <= 'd'). If it finds 4 or more nodes that meet this criteria, than you know it is within the boundary of the mesh. Obviously this could be applied to a body of multiple solid quad elements, however, at the edges, it might get a bit blurry so to speak. At the edges, there could be some cases where the coordinate is very close to the surface and outside of the boundary, but still in range of 4 nodes. The way to get more accurate results is by having a smaller mesh.
Let me know what you think. (this might be a long shot, but it's all I got).