Pairwise detect relations from Allen's Interval Algebra
Source:R/relation.R
allenrelationdetectpairwise.Rd
iv_pairwise_relates()
is similar to
iv_pairwise_overlaps()
, but it detects a specific set of relations
developed by James Allen in the paper: Maintaining Knowledge about Temporal Intervals.
Arguments
 x
[iv]
A pair of interval vectors.
These will be recycled against each other and cast to the same type.
 y
[iv]
A pair of interval vectors.
These will be recycled against each other and cast to the same type.
 ...
These dots are for future extensions and must be empty.
 type
[character(1)]
The type of relationship to find. See the Allen's Interval Algebra section for a complete description of each type. One of:
"precedes"
"precededby"
"meets"
"metby"
"overlaps"
"overlappedby"
"starts"
"startedby"
"during"
"contains"
"finishes"
"finishedby"
"equals"
Allen's Interval Algebra
The interval algebra developed by James Allen serves as a basis and
inspiration for iv_locate_overlaps()
, iv_locate_precedes()
, and
iv_locate_follows()
. The original algebra is composed of 13 relations
which have the following properties:
Distinct: No pair of intervals can be related by more than one
type
.Exhaustive: All pairs of intervals are described by one of the
type
s.Qualitative: No numeric intervals are considered. The relationships are computed by purely qualitative means.
Take the notation that x
and y
represent two intervals. Now assume that
x
can be represented as [x_s, x_e)
, where x_s
is the start of the
interval and x_e
is the end of it. Additionally, assume that x_s < x_e
.
With this notation, the 13 relations are as follows:
Precedes:
x_e < y_s
Precededby:
x_s > y_e
Meets:
x_e == y_s
Metby:
x_s == y_e
Overlaps:
(x_s < y_s) & (x_e > y_s) & (x_e < y_e)
Overlappedby:
(x_e > y_e) & (x_s < y_e) & (x_s > y_s)
Starts:
(x_s == y_s) & (x_e < y_e)
Startedby:
(x_s == y_s) & (x_e > y_e)
Finishes:
(x_s > y_s) & (x_e == y_e)
Finishedby:
(x_s < y_s) & (x_e == y_e)
During:
(x_s > y_s) & (x_e < y_e)
Contains:
(x_s < y_s) & (x_e > y_e)
Equals:
(x_s == y_s) & (x_e == y_e)
Note that when missing = "equals"
, missing intervals will only match
the type = "equals"
relation. This ensures that the distinct property
of the algebra is maintained.
Connection to other functions
Note that some of the above relations are fairly restrictive. For example,
"overlaps"
only detects cases where x
straddles y_s
. It does not
consider the case where x
and y
are equal to be an overlap (as this
is "equals"
) nor does it consider when x
straddles y_e
to be an
overlap (as this is "overlappedby"
). This makes the relations extremely
useful from a theoretical perspective, because they can be combined without
fear of duplicating relations, but they don't match our typical expectations
for what an "overlap" is.
iv_locate_overlaps()
, iv_locate_precedes()
, and iv_locate_follows()
use
more intuitive type
s that aren't distinct, but typically match your
expectations better. They can each be expressed in terms of Allen's
relations:
"any"
:overlaps  overlappedby  starts  startedby  finishes  finishedby  during  contains  equals
"contains"
:contains  startedby  finishedby  equals
"within"
:during  starts  finishes  equals
"starts"
:starts  startedby  equals
"ends"
:finishes  finishedby  equals
"equals"
:equals

precedes  meets

precededby  metby
Examples
x < iv_pairs(c(1, 3), c(3, 5))
y < iv_pairs(c(3, 4), c(6, 7))
# `"precedes"` is strict, and doesn't let the endpoints match
iv_pairwise_relates(x, y, type = "precedes")
#> [1] FALSE TRUE
# Since that is what `"meets"` represents
iv_pairwise_relates(x, y, type = "meets")
#> [1] TRUE FALSE
# `"during"` only matches when `x` is completely contained in `y`, and
# doesn't allow any endpoints to match
x < iv_pairs(c(1, 3), c(4, 5), c(8, 9))
y < iv_pairs(c(1, 4), c(3, 8), c(8, 9))
iv_pairwise_relates(x, y, type = "during")
#> [1] FALSE TRUE FALSE