Traditionally, geometric range queries are interested in finding objects which fall within a query region, e.g., points in a circle, line segments in a rectangle. If we are given a query region \(Q\), and an object \(o\), \(o\) should be considered if \(o \in Q\).
We consider a related problem where we wish to report objects which may be only partially within the query region. That is, given a query region \(Q\) and a fixed parameter \(\rho\), \(0 < \rho \leq 1\), we want to identify all objects where the proportion of the object found inside \(Q\) is at least \(\rho\) w.r.t. the size, area, etc. of the original object. E.g., for a line segment \(s\), we would include \(s\) if and only if \(|s \cap Q| \geq \rho |s|\).
We will give the details for several specific variations of the problem.