How to create mesh or contour plot for irregular spaced 2D data

I have a complex geometry, where I have exported X and Y coordinates with their respective U and V velocity components. However my geometry is not a simple rectangular geometry, having regions where there is no flow (and thus no velocity components). But when I use griddata, it seems that it is interpolating values from the empty region with NaN values to the actual flow region. Can someone help me?

[Sean de Wolski]

Please provide a small snippet of sample code/data. It is not clear what behavior is happening.