From: Pierre-Charles David <pcdavid@...>
Date: 2007-02-21T19:23:17+09:00
Subject: Re: Range#overlap?

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

-- 
http://pcdavid.net/