Can I determine farthest spot from multiple points?

[TiffanyFalk1]

Does anyone know a good tool or strategy for determining the following scenario: In a polygon there are multiple points in a single shapefile. Is there a way to figure out the spot/point in the polygon which is farthest away from all the points?

Thanks!

[DuncanHornby]

If you are wanting to find the edge of the polygon. An approach would be to explode your polygon vertices into points and then run the generate near tool, sorting on the distance field in a descending order. This would not find a point on the edge between two vertices but this may be sufficient for your needs?

When you run the generate near tool you can specify the near location as XY, then summarize that data by point ID and feed that into the XT to Line tool to create above.

If you are wanting to find any location within the polygon then run the Euclidean Distance tool using points and setting the extent to the polygon. Then clip that raster to the polygon. Finally you would identify the maximum cell value and you could then extract that pixel and optionally convert it to a point