DESCRIPTION

t.vect.mapcalc performs temporal and spatial overlay and buffer functions on space time vector datasets (STVDS) by using the temporal vector algebra. New STVDS can be created, which are expressions of existing STVDS.

PROGRAM USE

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

"result = expression"

The statement structure is similar to r.mapcalc, see r.mapcalc. Where result represents the name of a space time vector dataset (STVDS)that will contain the result of the calculation that is given as expression on the right side of the equality sign. These expression can be any valid or nested combination of temporal operations and spatial overlay or buffer functions that are provided by the temporal algebra.
The temporal vector algebra works with space time vector datasets only (STVDS). The algebra provides methods for map selection from STVDS 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. In addition the algebra provides the spatial operations for vector overlay and buffering. All these operations can be assigned to STVDS or to the resulting map lists of operations between STVDS.

As default, topological relationships between space time datasets will be evaluated only temporal. Use the s flag to activate the additionally evaluate the spatial topology based on the spatial extents of maps.

The expression option must be passed as quoted expression, for example: 
t.vect.mapcalc expression="C = A & B" basename=result
Where C is the new space time vector dataset that will contain maps with the basename "result" that represent the intersection of maps from STVDS A and equally temporal related maps from STVDS B.

The map basename for the result STVDS must always be specified.

Temporal vector algebra

The temporal vector algebra provides a wide range of temporal and spatial operators and functions that will be presented in the following section.

Temporal relations

Several temporal topology relations between space time datasets are supported: 
equals            A ------
                  B ------

during            A  ---- 
                  B ------

contains          A ------
                  B  ---- 

starts            A ----
                  B ------

started           A ------
                  B ----

finishs           A   ---- 
                  B ------

finished          A ------
                  B   ----

precedes          A ----
                  B     ----

follows           A     ----
                  B ----

overlapped        A   ------
                  B ------

overlaps          A ------
                  B   ------

over              booth overlaps and overlapped
The relations must be read as: A is related to B, like - A equals B - A is during B - A contains B

Topological relations must be specified in {} parentheses.

Temporal Selection

The temporal selection simply selects parts of a space time dataset without processing raster or vector data. The algebra provides a selection operator : that selects parts of a space time dataset that are temporally equal to parts of a second one by default. The following expression 
C = A : B
means: Select all parts of space time dataset A that are equal to B and store it in space time dataset C. The parts are time stamped maps.

In addition the inverse selection operator !: is defined as the complement of the selection operator, hence the following expression 
C = A !: B
means: select all parts of space time time dataset A that are not equal to B and store it in space time dataset (STDS) C.

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 topological relations, that must be separated by the logical OR operator | and the temporal selection operator. Both parts are separated by comma and surrounded by curly braces: {"topological relations", "temporal selection operator"}

Examples: 
C = A {equals,:} B
C = A {equals,!:} B
We can now define arbitrary topological relations using logical OR operator to connect them: 
C = A {equals|during|overlaps,:} B
Select all parts of A that are equal to B, during B or overlaps 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
Same for the complementary selection: 
C = A !: B
C = A {!:} B
C = A {equal,!:} B

Conditional statements

Selection operations can be evaluated within conditional statements. 
Note A and B can either be space time datasets or expressions.

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.
The conditions are comparison expressions that are used to evaluate space time datasets. Specific values of temporal variables are compared by logical operators and evaluated for each map of the STDS.

The supported logical operators: 
Symbol  description

  ==    equal
  !=    not equal
  >     greater than
  >=    greater than or equal
  <     less than
  <=    less than or equal
  &&    and
  ||    or
Temporal functions: 

td(A)                   Returns a list of time intervals of STDS A

start_time()            Start time as HH::MM:SS
start_date()            Start date as yyyy-mm-DD
start_datetime()        Start datetime as yyyy-mm-DD HH:MM:SS
end_time()              End time as HH:MM:SS
end_date()              End date as yyyy-mm-DD
end_datetime()          End datetime as  yyyy-mm-DD HH:MM

start_doy()             Day of year (doy) from the start time [1 - 366]
start_dow()             Day of week (dow) from the start time [1 - 7], the start of the week is Monday == 1
start_year()            The year of the start time [0 - 9999]
start_month()           The month of the start time [1 - 12]
start_week()            Week of year of the start time [1 - 54]
start_day()             Day of month from the start time [1 - 31]
start_hour()            The hour of the start time [0 - 23]
start_minute()          The minute of the start time [0 - 59]
start_second()          The second of the start time [0 - 59]
end_doy()               Day of year (doy) from the end time [1 - 366]
end_dow()               Day of week (dow) from the end time [1 - 7], the start of the week is Monday == 1
end_year()              The year of the end time [0 - 9999]
end_month()             The month of the end time [1 - 12]
end_week()              Week of year of the end time [1 - 54]
end_day()               Day of month from the start time [1 - 31]
end_hour()              The hour of the end time [0 - 23]
end_minute()            The minute of the end time [0 - 59]
end_second()            The second of the end time [0 - 59]
Additionally the number of maps in intervals can be computed and used in conditional statements.
The operator to count the number of maps is the hash #. 
A{contains,#}B
This expression computes the number of maps from space time dataset B which are during the time intervals of maps from space time dataset A.
A list of integers (scalars) corresponding to the maps of A that contain maps from B will be returned.

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

Temporal Operators

The temporal algebra defines temporal operators that can be combined later with spatial operators to perform spatio-temporal operations. The temporal operators process the time instances and intervals of temporal related maps. 

AND             &       Intersection 
OR              |       Union
DISJOINT OR     +       Disjoint union
LEFT REFERENCE  =       Use the time stamp of the left space time dataset

For example we can compute the intersection, union or disjoint union from time stamps of maps that temporally overlap, or we can just keep the time stamp of the left STDS.

Spatial vector operators

The module supports the following boolean vector operations: 
 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)
And vector functions: 
 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

Combinations of temporal, vector and select operators

We combine the temporal topology relations, the temporal operators and the spatial/select operators to create spatio-temporal operators: 
{"list of temporal relations", "temporal operator" "spatial or select operator"}

The spatial and the select operators can be used stand-alone. In this case the temporal topology relation "equal" and the temporal operator "left reference =" is assumed and used as default. This allows the convenient use of the spatial and select operators in case of space time vector datasets with equal time stamps. 

 ---------------------------------------
|   |  & |  | |  ^ |  ~ |  + |  : |  !: |
|---|----|----|----|----|----|----|-----|
| & | && | &| | &^ | &~ | &+ | &: | &!: |
| | | |& | || | |^ | |~ | |+ | |: | |!: |
| + | +& | +| | +^ | +~ | ++ | +: | +!: |
| = | =& | =| | =^ | =~ | =+ | =: | =!: |
 ---------------------------------------

Examples:

Spatio-temporal intersect all maps from space time dataset A with all maps from space time dataset B which have equal time stamps and are temporary before Jan. 1. 2005 and store them in space time dataset D. 
D = if(start_date() < "2005-01-01", A & B)
Buffer all vector points from space time vector dataset A and B with a distance of one and intersect the results with overlapping, containing, during and equal temporal relations to store the result in space time vector dataset D with intersected time stamps. 
D = buff_p(A, 1) {overlaps|overlapped|equal|during|contains,&&} buff_p(B, 1)
Select all maps from space time dataset B which are during the temporal buffered space time dataset A with a map interval of three days, else select maps from C and store them in space time dataset D. 
D = if(contain, td(buff_t(A, "1 days")) == 3, B, C)

REFERENCES

PLY(Python-Lex-Yacc)

SEE ALSO

t.select

AUTHOR

Thomas Leppelt, Soeren Gebbert, Thuenen Institut, Germany

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