A function is a piece of code that is called by name. It can be passed data to operate on (i.e. the parameters) and can optionally return data (the return value). All data that is passed to a function is explicitly passed.
A method is a piece of code that is called by a name that is associated with an object. In most respects it is identical to a function except for two key differences:
- A method is implicitly passed the object on which it was called.
- A method is able to operate on data that is contained within the class (remembering that an object is an instance of a class - the class is the definition, the object is an instance of that data).
(this is a simplified explanation, ignoring issues of scope etc.)
(StartA <= EndB) and (EndA >= StartB)
Proof:
Let ConditionA Mean that DateRange A Completely After DateRange B
_ |---- DateRange A ------|
|---Date Range B -----| _
(True if StartA > EndB
)
Let ConditionB Mean that DateRange A is Completely Before DateRange B
|---- DateRange A -----| _
_ |---Date Range B ----|
(True if EndA < StartB
)
Then Overlap exists if Neither A Nor B is true -
(If one range is neither completely after the other,
nor completely before the other,
then they must overlap.)
Now one of De Morgan's laws says that:
Not (A Or B)
<=> Not A And Not B
Which translates to: (StartA <= EndB) and (EndA >= StartB)
NOTE: This includes conditions where the edges overlap exactly. If you wish to exclude that,
change the >=
operators to >
, and <=
to <
NOTE2. Thanks to @Baodad, see this blog, the actual overlap is least of:
{ endA-startA
, endA - startB
, endB-startA
, endB - startB
}
(StartA <= EndB) and (EndA >= StartB)
(StartA <= EndB) and (StartB <= EndA)
NOTE3. Thanks to @tomosius, a shorter version reads:
DateRangesOverlap = max(start1, start2) < min(end1, end2)
This is actually a syntactical shortcut for what is a longer implementation, which includes extra checks to verify that the start dates are on or before the endDates. Deriving this from above:
If start and end dates can be out of order, i.e., if it is possible that startA > endA
or startB > endB
, then you also have to check that they are in order, so that means you have to add two additional validity rules:
(StartA <= EndB) and (StartB <= EndA) and (StartA <= EndA) and (StartB <= EndB)
or:
(StartA <= EndB) and (StartA <= EndA) and (StartB <= EndA) and (StartB <= EndB)
or,
(StartA <= Min(EndA, EndB) and (StartB <= Min(EndA, EndB))
or:
(Max(StartA, StartB) <= Min(EndA, EndB)
But to implement Min()
and Max()
, you have to code, (using C ternary for terseness),:
(StartA > StartB? Start A: StartB) <= (EndA < EndB? EndA: EndB)
Best Answer
This is my solution in python. Works with 3d points and you can simplify for 2d.
Test example with pictures to help visualize :)