How draw rectangles more without the others go far?

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  Hello
  I have 2 tables: T1 and T2:
  

  with T1 as
  (select 2 FromPeriod, 4 ToPeriod, 10 FromSum, 12 ToSum  from dual)
  select * from t1;
  
  
  with T2 as
  (select 1 FromPeriod, 2 ToPeriod, 9 FromSum, 5 ToSum  from dual
  union all
  select 1 FromPeriod, 3 ToPeriod, 9 FromSum, 4 ToSum  from dual
  union all
  select 2 FromPeriod, 5 ToPeriod, 9 FromSum, 11 ToSum  from dual
  union all
  select 2 FromPeriod, 5 ToPeriod, 11 FromSum, 12 ToSum  from dual)
  select * from t2;

  FromPeriod, ToPeriod are positive whole number without decimal point.
  FromSum, ToSum are positive numbers can have the comma.
  
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  But table T2 allows periods affecting somehow. You can see that T2 contains "FromPeriod-ToPeriod" = [1-2] and also [1-3] that touch each other.
  
  We can look at the two tables T1 and T2 as rectangles where X - axis is the values of the axes and the "FromPeriod-ToPeriod" is [FromSum, ToSum].
  I need sql/plsql algorithm that returns true if the rectangle of table T1 is discovered/filled with rectangles in table T2. If the rectangle in T1 is completely filled or even more filled than necessary, then algorithm should return true. If even a small neighborhood in rectangle T1 is not filled by rectangles in T2, then the algorithm must return false.
  
  As see you in the sample data, T1 has a rectangle: [2-4; 10-12] T2 contains 4 mentions that fill/overdraw this area defined by T1. So for the moment the algorithm must return true.
  
  I do not know how to write effective elsewhere such algorithm, can you help me?
  
  --
  At the moment I only came with such algorithm/query:
  
  Test1: this test should return true:

  --query: is rectangle [2-4;10-12] filled? -Yes.
  with T2 as
  (select 1 FromPeriod, 2 ToPeriod, 9 FromSum, 5 ToSum  from dual
  union all
  select 1 FromPeriod, 3 ToPeriod, 9 FromSum, 4 ToSum  from dual
  union all
  select 2 FromPeriod, 5 ToPeriod, 9 FromSum, 11 ToSum  from dual
  union all
  select 2 FromPeriod, 5 ToPeriod, 11 FromSum, 12 ToSum  from dual)
  select * from t2
  where (2 <= ToPeriod and 4 >= FromPeriod) -- x-axes overlapping
  and (10 <= ToSum and 12 >= FromSum)--y-axes overlapping
  ;--2 rows
  
  --
  
  2     5     9     11
  2     5     11     12

  I takes as input the T1 table horizontal axes (2, [4]) and research data table T2 that affect this horizontal axes, also the value axes is compared. But how then? There are 2 files, but it can give 10 stores overlap in the periods and amounts. How to determine now that rectange T1 is filled?
  
  Test2: This case should return false:

  --query: is rectangle [2-4;10-12] filled? -No.
  with T2 as
  (select 1 FromPeriod, 2 ToPeriod, 9 FromSum, 4 ToSum  from dual
  union all
  select 1 FromPeriod, 3 ToPeriod, 9 FromSum, 4 ToSum  from dual
  union all
  select 2 FromPeriod, 4 ToPeriod, 9 FromSum, 11 ToSum  from dual
  union all
  select 2 FromPeriod, 5 ToPeriod, 13 FromSum, 13 ToSum  from dual)
  select * from t2
  where (2 <= ToPeriod and 4 >= FromPeriod) -- x-axes overlapping
  and (10 <= ToSum and 12 >= FromSum)--y-axes overlapping
  ;--1 row.
  
  2     4     9     11

  Charles,

  I see 2 choices, but none is likely to evolve very well. The first can be with SQL - subdivision T1 into unit squares and see if everything not covered by T2:

  with T1 as
  (select 2 FromPeriod, 4 ToPeriod, 10.1 FromSum, 12 ToSum  from dual)
  , T1X as
  (select (FromPeriod+level)-1 as Period from T1 connect by level <= (ToPeriod-FromPeriod)+1)
  , T1Y as
  (select (FromSum+level*.01)-.01 as Summ from T1 connect by level <= (ToSum-FromSum+.01)/.01)
  , T1XY as (select Period,Summ from T1X,T1Y)
  ,T2 as
  (select 1 FromPeriod, 2 ToPeriod, 9.99 FromSum, 10.1 ToSum  from dual--satisfies sub-region [(2,2);(10.1,10.1)]
  union all
  select 1 FromPeriod, 2 ToPeriod, 9.99 FromSum, 10.11 ToSum  from dual--now satisfied sub-regions: [(2,2);(10.1,10.11)
  union all
  select 2 FromPeriod, 2 ToPeriod, 10 FromSum, 12.01 ToSum  from dual--now satisfied sub-regions: [(2,2);(10.1,12)
  union all
  select 3 FromPeriod, 4 ToPeriod, 10 FromSum, 11.99 ToSum  from dual--now satisfied sub-regions: [(2,2);(10.1,12)],[(3,4);(10,11.99)]
  union all
  select 4 FromPeriod, 4 ToPeriod, 10 FromSum, 13 ToSum  from dual--now satisfied sub-regions: all filled, return true
  )
  select Period,Summ from T1XY
  where not exists (
  select 1
  from T2
  where T2.FromPeriod<=T1XY.Period
  and   T2.ToPeriod>=T1XY.Period
  and   T2.FromSum<=T1XY.Summ
  and   T2.ToSum>=T1XY.Summ
  )
  ;
  

  The second option is more inspiring you described, using a recursive algorithm to subdivide the T1 into small rectangles for each rectangle in T2. For example:

  X(1)={[a,b;c,d]}
  
  Y={[e,f;g,h];[i,j;k,l]}
  
  X(2)={[a,e;c,g];[e,f;c,g];[f,b;c,g];[a,e;g,h];[f,b;g,h];[a,e;h,d];[e,f;h,d];[f,b;h,d]}
  or
  X(2)={[a,b;c,g];[a,b;h,d];[a,e;c,d];[f,b;c,d]}  -- this gives some overlap, but fewer rectangles and the algorithm still works.
  
  You would have to refine it to handle partial overlaps correctly, then drop areas that don't have a positive area. If
  X(2) becomes empty then it is fully covered. It might be most efficient to sort T2 in order of descending area.
  

  Kind regards
  Bob

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