Re: Biggest inscribing squares in a region

Mike Amling wrote:

Given is a set of rectilinear rectangles in the plane. For each point in
the union of the rectangles we search the size of the biggest square,
such that each point of the square is covered by at least one rectangle
in the set.

Are you sure your question matches what you're trying to find? Why
specify "For each point in the union of the rectangles" when "the
biggest square, such that ..." is the same square for each such point?

Ok. I forgot one condition:

Given is a set of rectilinear rectangles in the plane. For each point p in
the union of the rectangles we search the size of the biggest square S(p)
covering p, such that each point of S(p) is covered by at least one
rectangle in the set.

One example (each x corresponds to a unit square): The union of the
rectangles is:

XXXXXX
XXXXXX
XXXXXXXXXXXX
XXXXXXXXXXXX
XXXXXXX
XXXXXX

For the top left point the biggest square has a side length of 6 units.
For the bottom right point the square has only a side length of 1 unit. For
each point in one of the given unit squares the solution is equal.
Therefore I write the length of the biggest square in each unit square and
the solution looks like that:

666666
666666
666666344444
666666344444
3344444
444441


Greetings
Christoph
.

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