You can use the gdistance package to create a cost surface raster, then use the shortestPath function to compute the distances between all your data points. You then need to do your interpolation using that distance matrix as your distance metric and not pythagoras. I think gstat will let you feed in a distance matrix for kriging.
You'll probably also need ...
Soap-film smoothing using GAM's may work for you.
Powerpoint on method
R Package download (you will need both the soap and mgcv packages)
What you need to do is to separate a part of your input points (at least 10% of your data), then with the 90% data interpolate your variable (in your case spline with barriers).
After that you must validate your results using RMSE for example, save the 10% of your data in a new shapefile and use extract values to points in the toolbox (spatial analyst->...
Late but here is a suggestion. You can call Trace Geometric Network geoprocessing tool from ArcObjects and you can pass any IFeatureLayer in it as flags or barriers.
You should be able to create a point on selected water main using ICurve.QueryPoint and save this point to IFeatureLayer and use it as a flag. If you have some layer in your network which ...
I Have to say that this is very limited information to work with and the question seems a bit too general, but I would guess the following will be the solution to what you're asking:
Create an inverse of your barrier feature class: by clipping it from a rectangle feature class of the total extent of your research area
Use the Kriging tool in ArcMap (SA ...
So I've contacted the ESRI Support and the response was
They [ESRI Redlands] have advised "that the solve route task excludes
all edges that intersect barriers from it's calculations. Thus the
solver never encounters any barriers when trying to solve the route
and therefore cannot return which barriers were obstructing the route.
This would also ...
To leverage this functionality you must include appropriate corresponding attribute values for any barrier Graphics passed in your request.
see the discussion of added cost barriers ...
You need to turn your analysis to Raster.
Try the Proximity analysis set of tools found in ArcMap
You can use the Cost Allocation tool to set the barriers
I don't think that interpolation between points, unless you have really good coverage will work for minerals age. It seems that proximity polygons inside individual areas will do better job. With spare coverage it is worth to consider methods developed by Hutchinson (Australian university), where cotinious raster of something helps interpolate values at XY ...
Please check out the constrainedKriging package. According to the description:
The package supplies functions for two-dimensional spatial
interpolation by constrained,covariance-matching constrained and
universal (external drift) kriging for points or block of any shape
for data with a nonstationary mean function and an isotropic weakly