Changes between Version 1 and Version 2 of Grass7/TemporalGISAlgebra

Timestamp:

Jun 13, 2013, 1:35:02 AM (11 years ago)

Author:

mastho

Comment:

--

Grass7/TemporalGISAlgebra

@@ -1 +1 @@
 = Temporal GIS Algebra for Raster and Vector Data =
+
+Overview of the temporal algebra elements and concepts.
+
+== Temporal topology relations ==
+
+
+{{{
+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 A is related to B, like
+- A equals B
+- A is during B
+- A contains B
+
+Topological relations must be specified in {} parentheses
+
+{{{
+A {equals} B
+}}}
+
+Topological relations are always combined with other
+temporal operators in the {} parentheses
+
+== Temporal operators ==
+
+Temporal operators that work on time intervals 
+and instances of maps in space time datasets:
+
+'''Intersection &  '''       
+
+ Examples with time intervals a and b: 
+{{{
+ c <- a & b
+  a ------                              
+  b  ----                               
+  c  ----
+
+  a ----
+  b   ----
+  c   --
+
+  a ---
+  b    ---
+  c
+}}}
+'''Union |'''
+
+ Examples with time intervals a and b: 
+{{{
+c <- a | b
+  a ------                              
+  b  ----                               
+  c ------
+
+  a ----
+  b   ----
+  c ------
+
+  a ---
+  b    ---
+  c ------
+
+  a ---
+  b     ---
+  c
+}}}
+'''Disjoint Union +'''
+
+ Examples with time intervals a and b: 
+{{{
+ c <- a + b
+  a ------                              
+  b  ----                               
+  c ------
+
+  a ----
+  b   ----
+  c ------
+
+  a ---
+  b    ---
+  c ------
+
+  a ---
+  b     ---
+  c -------
+
+}}}
+'''Left Reference ='''
+
+ Examples with time intervals a and b: 
+{{{
+ c <- a = b
+  a ------                              
+  b  ----                               
+  c ------ 
+
+  a ----
+  b   ----
+  c ----  
+
+  a ---
+  b    ---
+  c ---   
+
+  a ---
+  b     ---
+  c ---
+}}}
+
+ The = operator ignores indexing operators for space
+ time datasets: A[i]
+
+
+Temporal selection operators to select parts of
+space time datasets:
+
+'''  Selection           :'''[[BR]]
+'''  Inverse selection  !:'''
+
+Temporal operators have no precedence.
+
+ Examples:
+
+ * Select all maps from space time dataset A that 
+   have equal time intervals with space time dataset B
+   and store them in space time datasets C.
+  
+{{{
+   C = A : B
+   C = A {:} B
+   C = A {=:} B
+   C = A {equals,:} B
+   C = A {equals,=:} B
+}}}
+
+ * Select all maps from space time dataset A that 
+   have unequal time intervals with space time dataset B
+   and store them in space time datasets C.
+  
+{{{
+   C = A !: B
+   C = A {!:} B
+   C = A {=!:} B
+   C = A {equals,!:} B
+   C = A {equals,=!:} B
+}}}
+
+ * Select all maps from space time dataset A that 
+   are during time intervals of space time dataset B
+   and store them in space time datasets C. Use
+   the time interval/instances of A in C.
+  
+{{{
+   C = A {during,:} B
+   C = A {during,=:} B
+}}}
+
+ * Select all maps from space time dataset A that 
+   are during time intervals of space time dataset B
+   and store them in space time datasets C. The maps
+   in C will have different time intervals as A or B using the union operator.
+   Hence they are unions between time intervals of A and B.
+  
+{{{
+   C = A {during,|:} B
+}}}
+
+ * Select all maps from space time dataset A
+   that are during B and during C and during D.
+   Store the resulting list of maps using the timer intervals/instances
+   of A in E.
+
+{{{
+   E = A {during,=:} B {during,=:} C {during,=:} D
+}}}
+
+Operator number of maps in interval  [[BR]]
+'''Number of maps #'''
+
+Compute the number of maps from space time dataset B that are 
+during the time intervals of maps from space time dataset A.
+{{{
+A{contains,#}B
+}}}
+This will return a list of integers (scalars) corresponding to the maps of
+A that contain maps from B.
+
+
+== Combination of temporal operators ==
+
+{{{
+ --------------
+|   |  : |  !: |
+|---|- --|-----|
+| & | &: | &!: |
+| | | |: | |!: |
+| + | +: | +!: |
+| = | =: | =!: |
+ --------------
+}}}
+
+
+== Logical operators ==
+
+{{{
+==    equal  
+!=    not equal  
+>     greater than
+>=    greater than or equal
+<     less than
+<=    less than or equal
+&&    and
+||    or
+
+}}}
+
+== Temporal functions ==
+
+Note a and b can either be space time datasets or expressions.
+
+{{{
+if                      decision option
+  if(x, a)              a if x not 0
+  if(x, a, b)           a if x not 0, b otherwise
+
+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
+
+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]            
+}}}
+
+Examples:
+  Select all maps from space time dataset A that have equal time stamps
+  with space time dataset B and C and are ealier that Jan. 1. 2005 and
+  store them in space time dataset D.
+
+{{{
+  D = if(start_date() < "2005-01-01"), A{equals,=:}B{equals,=:}C)
+}}}
+
+= Temporal Vector Algebra =
+
+Boolean vector operations:
+
+{{{
+AND             &       Intersection            (v.overlay operator=and)
+OR              |       Union                   (v.overlay operator=or)
+DISJOINT OR     +       Disjoint union          (v.patch)
+XOR             ^       Symmetric difference    (v.overlay operator=xor)
+NOT             ~       Complement              (v.overlay operator=not)
+}}}
+
+Vector functions:
+
+{{{
+buff_p(a, size)         Buffer the points of all maps from space time vector dataset a with size 
+buff_l(a, size)         Buffer the lines of all maps from space time vector dataset a with size 
+buff_a(a, size)         Buffer the areas of all maps from space time vector dataset a with size 
+}}}
+
+Examples:
+
+ * Create an intersection between all maps of space time dataset 
+   A and B that have equal time stamps.
+
+{{{
+   C = A & B
+   C = A {&} B
+   C = A {=&} B
+   C = A {equals,=&} B
+}}}
+
+ 
+ * Question: Meeting of two animals that occur when the distance between two sea elephants is less than 10 meters?
+   Space time vector dataset A and B contains the measured positions and time instances/intervals of two sea elephants.
+   The granularity of the space time vector datasets is 1h. We create a new space time vector dataset C that contains the
+   spatio-temporal intersections of the positions of the sea elephants.
+
+
+{{{
+   C = buff_p(buff_t(A, "2 hours"), 5) {over||equals,&&} buff_p(buff_t(B, "2 hours"), 5)
+}}}
+
+== Combinations of temporal and vector operators ==
+
+{{{
+ ---------------------------------------
+|   |  : |  !: |  & |  | |  ^ |  ~ |  + |
+|---|----|-----|----|----|----|----|----|
+| & | &: | &!: | && | &| | &^ | &~ | &+ |
+| | | |: | |!: | |& | || | |^ | |~ | |+ |
+| + | +: | +!: | +& | +| | +^ | +~ | ++ |
+| = | =: | =!: | =& | =| | =^ | =~ | =+ |
+ ---------------------------------------
+}}}
+
+= Temporal Raster Algebra =
+
+Arithmetic Operators:
+
+{{{
+Symbol  description     precedence
+
+  %     modulus         1
+  /     division        1
+  *     multiplication  1
+  +     addition        2
+  -     subtraction     2
+}}}
+
+Logical operators:
+
+{{{
+Symbol  description             precedence
+
+  ==    equal                   3
+  !=    not equal               3
+  >     greater than            3
+  >=    greater than or equal   3
+  <     less than               3
+  <=    less than or equal      3
+  &&    and                     4
+  ||    or                      4
+}}}
+
+Raster functions:
+
+{{{
+abs(x)                  return absolute value of x
+foat(x)                 convert x to foating point
+if decision options:
+  if(x)                 1 if x not zero, 0 otherwise
+  if(x,a)               a if x not zero, 0 otherwise
+  if(x,a,b)             a if x not zero, b otherwise
+int(x)                  convert x to integer [ truncates ]
+log(x)                  natural log of x
+log(x,b)                log of x base b
+max(x,y[,z...])         largest value of those listed
+median(x,y[,z...])      median value of those listed
+min(x,y[,z...])         smallest value of those listed
+round(x)                round x to nearest integer
+sqrt(x)                 square root of x
+tan(x)                  tangent of x (x is in degrees)
+not(x)                  1 if x is zero, 0 otherwise
+pow(x,y)                x to the power y
+rand(a,b)               random value x : a <= x < b
+round(x)                round x to nearest integer
+sin(x)                  sine of x (x is in degrees)
+sqrt(x)                 square root of x
+tan(x)                  tangent of x (x is in degrees)
+xor(x,y)                exclusive-or (XOR) of x and y
+isnull(x)              check if x = NULL
+}}}
+
+Internal variables:
+
+{{{
+row()                   current row of moving window
+col()                   current col of moving window
+x()                     current x-coordinate of moving window
+y()                     current y-coordinate of moving window
+ewres()                 current east-west resolution
+nsres()                 current north-south resolution
+null()                  NULL value
+}}}
+
+Combination of temporal and arithmetical raster operators:
+
+{{{
+ ---------------------------------------
+|   |  : |  !: |  % |  / |  * |  - |  + |
+|---|----|-----|----|----|----|----|----|
+| & | &: | &!: | &% | &/ | &* | &- | &+ |
+| | | |: | |!: | |% | |/ | |* | |- | |+ |
+| + | +: | +!: | +% | +/ | +* | +- | ++ |
+| = | =: | =!: | =% | =/ | =* | =- | =+ |
+ ---------------------------------------
+}}}
+
+Combination of temporal and logical raster operators:
+
+{{{
+ ------------------------------------------------
+|   |  : |  !: |  == |  != |  <= |  >= |  < |  > |
+|---|----|-----|-----|-----|-----|-----|----|----|
+| & | &: | &!: | &== | &!= | &<= | &>= | &< | &> |
+| | | |: | |!: | |== | |!= | |<= | |>= | |< | |> |
+| + | +: | +!: | +== | +!= | +<= | +>= | +< | +> |
+| = | =: | =!: | === | =!= | =<= | =>= | =< | => |
+ ------------------------------------------- ----
+}}}
+
+Note the combination of temporal and logical operators is only
+possible in reference time mode.
+
+
+