Interpolating between two polygons

[JamesHolmquist]

So I have two polygons, different shoreline reconstructions, one from 6,000 years ago, and one from 4,500 years ago.  I would like to linearly interpolate between these two layers and project the sea level at exactly 4,900 years ago.  Is there a simple way to do this.  The only thing I can think to do is manually calculating a series of points with the measure function and running a spline function or something? 

thanks!

James

[TrishRice]

So I have two polygons, different shoreline reconstructions, one from 6,000 years ago, and one from 4,500 years ago. I would like to linearly interpolate between these two layers and project the sea level at exactly 4,900 years ago. Is there a simple way to do this. The only thing I can think to do is manually calculating a series of points with the measure function and running a spline function or something?

Which measure function do you mean?  If you literally mean measuring the distance with the little ruler, it can be way easier than that.  Here are two ideas.

1. Create a series of regular lines crossing both polygons.  Create points where they intersect the polygons (variety of ways to do that).  For each line interpolate a new point between those endpoints (can be done in Excel, or Field Calculator depending how you organize the data).  Create a line from those new points.  Here is a concept sketch to find the middle. This would work best if your data is pretty general, where there would only be one intersection between each polygon and the crossing line.  Not so great if you have capes, bays, etc, but it could probably work on those if you do multiple iterations with lines crossing the polygons at various angles.
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2. Convert the shorelines into points and do a Raster Interpolation.  Classify or Reclassify the raster data to get a convenient class break at 4900 years ago.  Convert the raster back to polygons.  (This requires Spatial Analyst.)

[michaelcollins1]

Similarly, convert the polygons to polylines, and use Topo to Raster interpolation with the two resultant 6000 and 4500 year isolines, then convert the raster back to isolines using say 100 year intervals. This would technically solve your problem, but then you're assuming that the temporal shoreline changes and slopes are constant. Perhaps it's as simple as saying the change is x metres per year, then use whatever contour line falls on the 4900 year level (assuming that you already have contours or a DEM of the area).