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I am trying to generate a fishnet/grid along a line/polyline or polygon boundary in ArcGis 10.3 or QGIS. While it is totally intuitive and easy to generate a box-standard grid, what I am trying to do is to basically generate a series of cells along the boudary of the Italian peninsula. One grid should have the center of each cell positioned along the boundary itself, and a second grid shoud have cells along the boundary but tangent to the boundary itself.

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I'd suggest creating a grid to encompass the entire boundary feature to the width and height appropriate for your analysis

I would then convert the boundary to a line feature

Then I would either select the grid cells that intersect the line feature, or buffer the line by a distance to grab a few more grid cells.

Then save those selected grid cells to a new dataset

I don't think you're ever going to be able to shift each grid cell so its center is located exactly along the coastline...

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