I am trying to use the new Region tools in Mathematica 10 with Interpolation functions. This is just a simple demo showing where I am stuck. We create points on a unit circle, then create Interpolation functions through the points. Then create a region, a circle, which plots fine.
data = Table[{Cos[2 Pi u], Sin[2 Pi u]}, {u, 0, 1, .01 }];
circ[u_] := {
ListInterpolation[data[[All, 1]], {{0, 1}}][u],
ListInterpolation[data[[All, 2]], {{0, 1}}][u]};
region = ParametricRegion[circ[u], {{u, 0, 1}}] ;
RegionPlot[region]
The RegionEmbeddingDimension routine works as expected.
RegionEmbeddingDimension[region]
But the RegionDimension routine silently fails, the kernel crashes and restarts, because the next output is labelled Out[1].
RegionDimension[region]
And now our region is undefined, since a new kernel is running.
region
Not having much joy with most other Region routines (like RegionDistance) on this Interpolation - based ParametricRegion. Any clues on what's going on here would be appreciated. Needless to say, my goal here is not to draw circles, but to create and manipulate geometry for CAD from images. I am using Version 10.0 for Mac OS X x86 (64-bit) (June 29, 2014).
