How to Convert from Point to Continuous Raster in ArcGIS 10.1?

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I have a vector point dataset that I would like to convert to raster. The point-to-raster conversion tool creates a raster grid with spaces between each grid cell. I want to create a 'continuous' raster whereby each grid cell expands outwards until its' borders meet with the adjacent cell's borders.

I find the interpolation tools under spatial analysis to be unsatisfactory (spline is the closest I come to satisfactory). I do not want to smooth my data when I put it in raster form (ie I want to keep peaks and valleys in data).

Is there a geoprocessing tool that gets at what I am attempting to do?



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