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Want to generate a point layer, that contains the maximum points in a polygon layer. all points should have the distance of 6 meters between each other. how can i do it?

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You can use the Fish net tool with 3 x 3 as cell size and set labels parameter to LABELS, or use the Feature to point tool with Centroid parameter. then Clip points based on polygon boundary

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Feature To Point would push you to an ArcInfo/Advanced level license - to avoid that when you use Create Fishnet make sure you choose POLYLINE and to have Labels created. – PolyGeo Mar 27 '13 at 10:16
@riesentoast I'm assuming that a Clip of fishnet points created in this way using your polygon layer will meet your requirements. – PolyGeo Mar 27 '13 at 10:24
for polyline option, i think that we should add intersection between those lines. – geogeek Mar 27 '13 at 10:29
I think asker is only interested in the point feature class (labels) and will be throwing away the polylines. – PolyGeo Mar 27 '13 at 10:32
I think it would be beneficial to update the post to 1) Include Labels (points) and 2) Clip points based on polygon boundary. – Aaron Mar 27 '13 at 13:00

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