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Triangulated Irregular Networks. Under what conditions is one sampling method more appropriate over the other?

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Equal sampling, while easier, means that you can either over-sample parts of the landscape that don't vary much (i.e. smooth slopes or completely flat land), or under-sample parts with a lot of variation (e.g. jagged mountain slopes). That is, you may waste time collecting measurements of no real importance or miss out on important information, respectively.

If the area you are interested in contains land in both of these categories, an unequal sampling will allow you to collect a denser set of samples over the jagged areas, while not wasting the effort over the smooth areas (since there is no practical benefit to densely sampling them for a TIN). If the entire area is jagged, a regular sampling grid (albeit a dense one) will be fine; a very spaced-out regular sampling grid would be fine for an area that was all smooth.

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