How to align shapefile layers

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Ishaan Chauhan
Ishaan Chauhan 2021-2-23
I currently have a problem where my shapefile layers do not align, is there any way to get them to align without changing the shapefile itself?
These are meant to be the same islands/area, but they do not align
I'm using a third-party coastlines shapefile dataset(https://www.naturalearthdata.com/downloads/50m-physical-vectors/), as the Matlab one just didn't include half the islands in my 1x1 square. This high res one is still missing an island. (left image)
I'm also using a third-party roads shapefile (https://sedac.ciesin.columbia.edu/data/set/groads-global-roads-open-access-v1/data-download) for the same reason.
using a hgt file for the topography on the right, which I've read in and I'm using MeshGrid for

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