Algorithm required to determine if a rectangle is completely covered by another set of rectangles

Question

I am searching for an algorithm that will determine if a new rectangle is completely covered by a set of existing rectangles. Another way of putting the question, is does the ne

Answer 1

If rectangles are aligned that's easy:

Let's say you have rectangle A0 and want to know if it is fully covered by (B1, B2, B3...) = B

A := (A0)
while P := pop B
  for R in A
    if P fully covers R:
      remove R from A
    else if P and R does overlap:
      remove R from A
      break R in subrentangles S := (S1, S2, S3,...) following the intersections \
                                                     with P edges
      push S into A
if A is empty:
   say B covers A0
else:
   say B does not fully cover A0