From: Daniel Finnie <danfinnie@...>
Date: 2007-02-23T04:51:01+09:00
Subject: Re: Range#overlap?

I have made some tests for the code and shown the results at 
http://pastie.caboo.se/42266 .  Please check the assertions with # I 
assume by them, the paper referenced went way over my head.

Dan

Pierre-Charles David wrote:
> FWIW, people working with temporal logics and event algebras define 13
> possible relationships between two intervals (see Fig. 4 page 10 of
> [1]), with a precise (if not always intuitive) vocabulary.
> 
> In Ruby, these would be (not tested):
> 
> class Range
>  # self:   |---|
>  # other:         |---|
>  def before?(other)
>    self.end < other.begin
>  end
> 
>  # self:          |---|
>  # other:  |---|
>  def after?(other)
>    other.before? self
>  end
> 
>  # self:  |---|
>  # other:     |---|
>  def meets?(other)
>    self.end == other.begin
>  end
> 
>  # self:      |---|
>  # other: |---|
>  def met_by?(other)
>    other.meets?(self)
>  end
> 
>  # self:  |---|
>  # other:   |---|
>  def overlaps?(other)
>    (self.begin < other.begin) and other.include?(self.end)
>  end
> 
>  # self:    |---|
>  # other: |---|
>  def overlapped_by?(other)
>    other.overlaps?(self)
>  end
> 
>  # self:  |-----|
>  # other:   |---|
>  def finished_by?(other)
>    (self.begin < other.begin) and (self.end == other.end)
>  end
> 
>  # self:  |-----|
>  # other: |---|
>  def started_by?(other)
>    (self.begin == other.begin) and (self.end > other.end)
>  end
> 
>  # self:  |---|
>  # other: |-----|
>  def starts?(other)
>    other.started_by?(self)
>  end
> 
>  # self:    |---|
>  # other: |-----|
>  def finishes?(other)
>    other.finished_by?(self)
>  end
> 
>  # self:  |-------|
>  # other:   |---|
>  def contains?(other)
>    (self.begin < other.begin) and (self.end > other.end)
>  end
> 
>  # self:   |---|
>  # other:  |---|
>  def equals?(other)
>    (self.begin == other.begin) and (self.end == other.end)
>  end
> 
>  # self:     |---|
>  # other:  |-------|
>  def during?(other)
>    other.contains?(self)
>  end
> end
> 
> [1] Allen, J.F. and Ferguson, G. Actions and Events in Interval
> Temporal Logic, J. Logic and Computation 4, 5, 1994.
> http://tinyurl.com/2twek7
>