**-s**- Check the spatial topology of temporally related maps and process only spatially related maps
**--help**- Print usage summary
**--verbose**- Verbose module output
**--quiet**- Quiet module output
**--ui**- Force launching GUI dialog

**expression**=*expression***[required]**- Spatio-temporal mapcalc expression
**basename**=*basename***[required]**- Basename of the new generated output maps
- A numerical suffix separated by an underscore will be attached to create a unique identifier

The module expects an **expression** as input parameter in the following form:

"result = expression"

The algebra provides methods for map selection from STDS based on their temporal relations. It is also possible to temporally shift maps, to create temporal buffer and to snap time instances to create a valid temporal topology. Furthermore expressions can be nested and evaluated in conditional statements (if, else statements). Within if-statements the algebra provides temporal variables like start time, end time, day of year, time differences or number of maps per time interval to build up conditions. These operations can be assigned to space time datasets or to the results of operations between space time datasets.

As default, topological relationships between space time datasets
will be evaluated only temporal. Use the **s** flag to activate the
additionally spatial topology evaluation.

The expression option
must be passed as **quoted** expression, for example:

t.select expression="C = A : B"

equals A ------ B ------ during A ---- B ------ contains A ------ B ---- starts A ---- B ------ started A ------ B ---- finishes A ---- B ------ finished A ------ B ---- precedes A ---- B ---- follows A ---- B ---- overlapped A ------ B ------ overlaps A ------ B ------ over booth overlaps and overlapped

Topological relations must be specified in {} parentheses.

LEFT REFERENCE l Use the time stamp of the left space time dataset INTERSECTION i Intersection DISJOINT UNION d Disjoint union UNION u Union RIGHT REFERENCE r Use the time stamp of the right space time dataset

C = A : B

In addition the inverse selection operator **!:** is defined as
the complement of the selection operator, hence the following
expression

C = A !: B

To select parts of a STDS by different topological relations to other
STDS, the temporal topology selection operator can be used. The
operator consists of the temporal selection operator, the topological
relations, that must be separated by the logical OR operator **|**
and the temporal extent operator. All three parts are separated by
comma and surrounded by curly braces:

{"temporal selection operator", "topological relations", "temporal operator"}

Examples:

C = A {:, equals} B C = A {!:, equals} B

C = A {:,equals|during|overlaps} B

In addition we can define the temporal extent of the result STDS by adding the temporal operator.

C = A {:, during,r} B

The selection operator is implicitly contained in the temporal topology selection operator, so that the following statements are exactly the same:

C = A : B C = A {:} B C = A {:,equal} B C = A {:,equal,l} B

C = A !: B C = A {!:} B C = A {!:,equal} B C = A {!:,equal,l} B

Note A and B can either be space time datasets or expressions. The temporal relationship between the conditions and the conclusions can be defined at the beginning of the if statement. The relationship between then and else conclusion must be always equal.

if statement decision option temporal relations if(if, then, else) if(conditions, A) A if conditions are True; temporal topological relation between if and then is equal. if(conditions, A, B) A if conditions are True, B otherwise; temporal topological relation between if, then and else is equal. if(topologies, conditions, A) A if conditions are True; temporal topological relation between if and then is explicit specified by topologies. if(topologies, conditions, A, B) A if conditions are True, B otherwise; temporal topological relation between if, then and else is explicit specified by topologies.

Symbol description == equal != not equal > greater than >= greater than or equal < less than <= less than or equal && and || or

td(A) Returns a list of time intervals of STDS A start_time(A) Start time as HH::MM:SS start_date(A) Start date as yyyy-mm-DD start_datetime(A) Start datetime as yyyy-mm-DD HH:MM:SS end_time(A) End time as HH:MM:SS end_date(A) End date as yyyy-mm-DD end_datetime(A) End datetime as yyyy-mm-DD HH:MM start_doy(A) Day of year (doy) from the start time [1 - 366] start_dow(A) Day of week (dow) from the start time [1 - 7], the start of the week is Monday == 1 start_year(A) The year of the start time [0 - 9999] start_month(A) The month of the start time [1 - 12] start_week(A) Week of year of the start time [1 - 54] start_day(A) Day of month from the start time [1 - 31] start_hour(A) The hour of the start time [0 - 23] start_minute(A) The minute of the start time [0 - 59] start_second(A) The second of the start time [0 - 59] end_doy(A) Day of year (doy) from the end time [1 - 366] end_dow(A) Day of week (dow) from the end time [1 - 7], the start of the week is Monday == 1 end_year(A) The year of the end time [0 - 9999] end_month(A) The month of the end time [1 - 12] end_week(A) Week of year of the end time [1 - 54] end_day(A) Day of month from the start time [1 - 31] end_hour(A) The hour of the end time [0 - 23] end_minute(A) The minute of the end time [0 - 59] end_second(A) The second of the end time [0 - 59]

The structure is similar to the select operator with the extension of an aggregation operator:

{"comparison operator", "topological relations", aggregation operator, "temporal operator"}

This aggregation operator (| or &) define the behaviour if a map is related the more than one map, e.g for the topological relations 'contains'. Should all (&) conditions for the related maps be true or is it sufficient to have any (|) condition that is true. The resulting boolean value is then compared to the first condition by the comparison operator (|| or &&). As default the aggregation operator is related to the comparison operator:

Comparison operator -> aggregation operator:

|| -> | and && -> &

Condition 1 {||, equal, r} Condition 2 Condition 1 {&&, equal|during, l} Condition 2 Condition 1 {&&, equal|contains, |, l} Condition 2 Condition 1 {&&, equal|during, l} Condition 2 && Condition 3 Condition 1 {&&, equal|during, l} Condition 2 {&&,contains, |, r} Condition 3

A{#, contains}B

A list of integers (scalars) corresponding to the maps of A that contain maps from B will be returned.

C = if({equal}, A {#, contains} B > 2, A {:, contains} B)

Furthermore the temporal algebra allows temporal buffering, shifting and snapping with the functions buff_t(), tshift() and tsnap() respectively.

buff_t(A, size) Buffer STDS A with granule ("1 month" or 5) tshift(A, size) Shift STDS A with granule ("1 month" or 5) tsnap(A) Snap time instances and intervals of STDS A

tmap()

C = A {:,during} tmap(event)

Boolean Name Operator Meaning Precedence Correspondent function ---------------------------------------------------------------------------------- AND & Intersection 1 (v.overlay operator=and) OR | Union 1 (v.overlay operator=or) DISJOINT OR + Disjoint union 1 (v.patch) XOR ^ Symmetric difference 1 (v.overlay operator=xor) NOT ~ Complement 1 (v.overlay operator=not)

buff_p(A, size) Buffer the points of vector map layer A with size buff_l(A, size) Buffer the lines of vector map layer A with size buff_a(A, size) Buffer the areas of vector map layer A with size

{"spatial or select operator" , "list of temporal relations", "temporal operator" }

For multiple topological relations or several related maps the spatio-temporal operators feature implicit aggregation. The algebra evaluates the stated STDS by their temporal topologies and apply the given spatio temporal operators in a aggregated form. If we have two STDS A and B, B has three maps: b1, b2, b3 that are all during the temporal extent of the single map a1 of A, then the following overlay calculations would implicitly aggregate all maps of B into one result map for a1 of A:

C = A {&, contains} B --> c1 = a1 & b1 & b2 & b3

C = B {&, during} A --> c1 = b1 & a1 c2 = b2 & a1 c3 = b3 & a1

D = if(start_date(A) < "2005-01-01", A & B)

D = buff_p(A, 1) {&,overlaps|overlapped|equal|during|contains,i} buff_p(B, 1)

D = if(contains, td(buff_t(A, "1 days")) == 3, B, C)

Available at: t.vect.algebra source code (history)

Latest change: Thursday Jan 26 14:10:26 2023 in commit: cdd84c130cea04b204479e2efdc75c742efc4843

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