Which operator will select a target feature based on its centroid?

The operator that selects a target feature based on its centroid is "Have their centroid within." This operator specifically looks at the centroids of features, which are the geometric centers of the features. When using this operator, the focus is on whether the centroid of one feature lies within the boundaries of another feature. This means that if you want to select features based on the position of their centroids in relation to the boundaries of other features, this is the appropriate choice.

Understanding centroids is crucial in spatial analysis, as they often represent the point location of a feature in mapping and spatial decision-making. The use of this operator is especially useful in applications where the centrality of a feature, rather than its overall area or perimeter, is of interest.

In contrast, the other operators mentioned either relate to line segments or edges, or concern more general aspects of the spatial relationship rather than focusing specifically on the centroid's location. Thus, "Have their centroid within" accurately captures the intention of selecting features based on their centroids in a spatial query context.