确定矩形是否被一组多边形完全覆盖所需的算法

Question

Given a set of polygons P and a rectangular area A, I need to verify if A is completely covered by P.

The number and complexity of the polygons and the total area A are significantly large and so, a polygon union-based approach might not work in time. To make things a bit simpler, I defined A' as the size of the smallest area inside A whose coverage I care about. I thought of building up a 2D segment-tree like structure dividing the area in 2D repeatedly(each area square breaks into 4 child squares until the child square size is A') but since we are dealing with polygons here, I am not sure if this would be efficient enough.

Answer 1

You can use polygon intersection or difference instead of union:

Consider A itself as a polygon and each time pick a polygon P' and refine A as A - P', and check to see if A is empty. After checking all polygons you can say for sure whether A is covered by P or not.