GEOG 2GI3 Lecture Notes - Lecture 3: Simple Polygon, Digital Elevation Model, Raster Graphics
18 May 2018
School
Department
Course
Professor
How$are$Data$Represented$in$a$GIS?
Data$model:$set$of$constructs$for$representing$the$"real$world"$in$the$digital$
environment$of$a$GIS
•
Geography$is$represented$as$either$objects(or(fields
•
Objects,$Fields$and$Data$Models
Discrete$entities;$well-defined$boundaries
•
Recognizable$classes
•
Countable
•
0-dimensional
○
1-dimensional$lines
○
2-dimensional$areas$(polygons)
○
Dimensionally$defines$three$primitives
•
Objects
Variables$change$in$value$at$all$locations
○
Continuous$surface
•
Values$that$exist$virtually$everywhere
•
Ex.$Soil$properties,$elevation,$precipitation
•
Fields
Vector$Representation:$what$each$colour$represents$(dark$green=$forest,$
blue=water,$
•
Raster:$defined$by$pixels;$pixelated;$not$as$clean$boundaries$potentially
•
Elevation:$contour$lines=vector,$pixels=raster
•
Land$use:$Raster=right
•
Buildings:$Raster=$left
•
Representation$Examples
Vector$Data$Model
Represents$discrete$objects
•
Vectors$better$for$defining$boundaries$more$precisely
§
Precise$nature$of$its$representation$method
○
Quality$of$cartographic$output
○
Only$tells$you$"what$is$where"
§
Raster$tells$you$"what$is$everywhere"$;$even$if$nothing$there,$a$pixel$
represents$that$data
§
Storage$efficiency
○
Topology
○
Widely$implemented
•
Space$defined$by$continuous$XY$coordinates•
Object$locations$defined$by$XY$coordinate$pairs•
Coordinate$pairs$are$used$as$building$blocks$for$more$complex$features;$lines$
and$polygons
•
Vector$Representation
Point$data$set•
Locating$specific$objects•
Identifier$and$coordinate$pair$needed•
Utility$companies:$mapping$•
Points
Points$connected$together•
One/several$segments=$arc•
Endpoints$of$arc$are$nodes•
Angle$points$are$vertices•
Feature$starts$and$ends$with$a$node
○
Feature$is$defined$by$the$arc,$not$the$line•
Two$arcs$meet$at$the$nodes•
Lines
Perfectly$enclosed•
Simple$polygon:$composed$with$lines$with$common$beginning/ending$node•
Complex$polygon:$contains$"islands";$definition$of$"inside"$is$more$complex•
Ex.$S.$Africa•
Polygons
Topology
Mathematical$procedure$for$defining$spatial$relationships;$i.e.$mathematics$of$
connectivity$and$adjacency$for$spatial$features$(how$features$join)
•
Validate$geometry$of$vector$datasets$(check$to$see$polygons$are$closed,$
lines$are$connected,$etc.$
○
Various$operations$(spatial$search,$shortest$path,$etc)
○
Used$in$GIS:•
If$topology$in$effect,$projections$do$not$alter$facts$(ex.$Continguous$$polygons)•
Knows$where$it$is
○
Knows$what$is$around$it
○
Has$recognized$spatial$relationships$with$other$features
○
Has$length,$distance,$perimeter$and$area$information
○
Knows$how$to$get$around
○
Understands$its$environment
○
With$topology,$each$feature$has$the$following$characteristics•
Can$be$used$to$identify$spatial$associations$between$or$among$geographic$
features
•
Containment;$something$within$something$else$(counties$have$to$be$
within$province)
○
Adjacency/proximity
○
Connectivity
○
Intersection/overlap
○
Types$of$spatial$association•
How$do$spatial$patterns$and$distributions$of$volcanoes$relate$to$location$
of$tectonic$boundaries
○
Topology$helps$us$see$that
○
Proximity•
Overpass$vs.$intersection$represented$with$nodes$or$not
○
Interchanges$for$highways;$what$is$actually$intersecting$vs.$overpasses
○
Intersection$and$overlap•
Topology
How$we$create$topology•
Representation$of$vector$objects$in$computer•
Vector$Encoding
Bunch$of$overlapping$lines
○
Simple$structure
○
List$of$coordinates,$with$lots$of$duplication$particularly$in$polygon$data$
sets
○
Each$feature$has$no$knowledge$of$other$features$that$it$intersects,$
is$adjacent$to,$contiguous$with$or$near
§
No$relative$relationships$encoded$in$this$model
○
Generally$come$from$CAD$files
○
Non-topological$data$model•
Spaghetti$Data$Model
"arc-node$model"•
Points=$lowercase$letters$(blue$and$green)•
Arrows$showing$direction$of$encoding•
Done$feature$by$feature:$•
Topological$Data$Model
XY$coordinate$for$each$point•
Node$File
From-node,$To-node,$vertices,$Left$polygon,$Right$polygon$(polygons$oriented$
based$on$direction$of$encoding)
•
Blue=nodes,$green=vertices•
*Defined$by$system*•
Coverage:$topological$data$structure$(folder);$where$you$find$table$of$Arc$info$
(.aat)
•
Shapefiles:$non-topological$structure;$series$of$connected$arcs,$polygons$or$
points
•
Geodatabase:$topological;$based$on$common$language$rules;$putting$topological$
data$into$semantic$language$
•
Arc$File
Identifier$for$polygon$and$arcs$that$make$up$polygons•
"0"$indicates$what$follows$is$within$polygon•
Polygon$File
Shapefiles,$coverages
§
Spatial$and$attribute$data
§
Geo-spatial$part
§
Relational-database$part
§
Classical$approach$to$vector$data
§
Georelational$
○
Spatial$and$tabular$components$are$stored$in$single$system
§
Spatial$features$can$have$properties$and$methods
§
Recent$trends$towards$object-based$models
§
Specific$behaviours$modelled
§
Object-based
○
Two$Common$Methods•
Storing$Vector$Data
Raster$Data$Model
R$data$model$used$to$represent$both$fields$and$objects•
Degree$of$generalization$for$linear$features$depends$on$pixel$sizes•
Divides$space$into$series$of$units$(grid$cells)
○
Each$unit$same$in$size
○
Cellular$organization•
Every$pixel$ needs$a$value
○
JPEG,$GIF,$BMP,$and$TIF$are$raster$formats
○
Each$pixel$ encoded$with$specific$value•
Used$to$represent$digital$orthophotos,$DEMS,$categorical$data,$multispectral$
images,$etc
•
Raster$Representation
Assigned$one$value$only•
How$do$you$assign$values$to$cells$containing$more$than$one$feature
○
Mixed$pixel$problem:•
Value$of$a$cell$may$be$based$on$a$domination$scheme,$the$commonest$
value$in$the$cell,$or$the$edge$itself
○
May$also$be$the$value$found$at$the$cell's$central$point
○
Assignment$scheme•
Cell$Values
Values$are$integers•
Refers$to$limited$number$of$classes•
Pixels$with$same$value$equals$same$class•
Similar$to$polygons•
Ex.$Soild$class,$vegetation$class•
Discrete$Raster
Any$values$within$a$range
○
decimals
○
Values$are$floating$point•
Also$called$surface•
Digital$elevation$model
○
Ex.$Elevation,$precipitation,$air$pollution•
Continuous$Raster
If$projected,$origin$is$bottom$left
§
Origin$of$raster$is$upper$left$corner$(unprojected)
○
Not$stored$as$XY;$cell$has$an$implied$location;$only$grid$origin$is$stored•
Locational$precision$is$based$on$cell$size•
Cell$location$refers$to$center$of$cell•
Locational$Precision
Size$of$grid$cell$ or$picture$element,$defining$level$of$spatial$detail$in$
ground$units
○
Pixel$size=$Minimum$Mapping$Unit=$$resolution
○
Variation$within$pixels$is$lost;$coarser$the$resolution$the$less$variation
○
Resolution$(pixel$size)•
Increase$detail$by$decreasing$pixel$size•
Can$effectively$replicate$ vector$structures$with$small$enough$grid$cell$sizes•
Level$of$detail$required
○
Features$being$mapped
○
Storage$available$and$machine$speed
○
Decision$based$on:•
Tradeoff$between$detail$and$storage•
Resolution
1/2$pixel$width=$4x$data$volume•
Lots$of$variability=$need$smaller$pixels•
Data$Volume
No$compression
○
Just$a$line-scan
○
"AAAAABBBAABBAAAB"
○
Worst$case
○
Sequential$encoding•
Everything$along$a$line
○
Scans$across$rows
○
If$identical$pixels,$represented$by$number$of$consecutive$pixels
○
Each$row$separated
○
Ex.$First$row$has$7$A's$in$a$row:$7A
○
Run$length•
Cuts$across$different$rows
○
If$identical$throughout$rows,$represented$by$number$of$consecutive$rows
○
Continuous$zig-zag$pattern
○
Row$order•
Cuts$across$rows,$follows$down$to$next$row$vertically
○
Not$a$zig$zag$pattern
○
Row$prime$order•
Example•
AAAA
A B B B
A A B B
AAAB
AAAAABBBAABBAAAB
○
Sequential$(16)•
4A$1A$3B$2A$2B$3A$1B
○
Run$Length$(14)•
5A$3B$2A$2B$3A$1B
○
Run$Length-Row$Order$(12)•
4A$3B$3A$3B$3A$(top$left)
○
5A$5B$5A$1B$(top$right)
○
Run$Length-Row$Prime$Order$(10$or$8)•
Data$Compression
Uses$cells$of$different$sizes$depending$upon$information$density•
Large$cells$in$smooth$areas,$small$ones$in$highly$variable$areas•
More$efficient$storage$than$run-length$encoding•
Makes$display$analysis$faster•
Quadtree$Data$Model
Divide$into$4$quadrants
○
If$quadrant$is$homogenous$then$leave$as$is
○
A$quadrant$is$homogenous
§
OR
Highest$level$ of$resolution$is$reached
§
Otherwise,$recursively$subdivide$until
○
Summary:•
Building$a$Quadtree
Root$into$Leaf$into$Node•
If$odd$number$of$rows$or$columns,$system$will$add$blank$"no$data"$row$and$
column$to$be$able$to$divide$evenly
•
Quadtree$Organization
Raster$vs.$Vector
Point•
Simple$line•
Complex$line•
Single$polygon•
Connected$polygons•
Raster$and$Vector$Data$Structure
If$discrete,$vector$the$better$one
§
Discreteness$of$entity$being$depicted
○
Certain$only$applicable$by$one$or$the$other
§
Ex.$Road$networks$and$shortest$path:$vector$better$
§
Intended$applications
○
Vector$based$map$(road$map)
§
Source$data
○
Vector$data$is$smaller,$compact$(especially$in$.gdb)
§
Raster$has$to$tell$us$everything$in$study$area,$even$if$not$relevant;$
files$considerably$larger
§
Storage$considerations
○
Must$consider•
Considerations
Good$representation$of$reality
○
More$efficient$data$storage
○
Topology$can$be$described$as$network
○
Accurate$graphics
○
Variety$of$attributes$can$be$associated$with$one$feature
○
Feature$based$processing
○
Advantages•
Complex$data$structures
○
Simulation$may$be$difficult
○
Some$spatial$analysis$operations$are$difficult$or$impossible$to$perform
○
Disadvantages•
Advantages$and$Disadvantages:$Vector
Easy$overlay
○
Simple$data$structure,$geographic$position$is$implicit
○
Various$kinds$of$spatial$analysis$available
○
Uniform$size$and$shape
○
Can$accommodate$both$discrete$and$continuous$features
○
Compatible$with$remotely$sensed$data
○
Advantages•
Large$amount$of$data
○
Less$"pretty"
○
Projection$transformation$is$more$difficult
○
Different$resolutions$between$layers$may$be$a$nightmare
○
May$lose$information$due$to$generalization
○
Disadvantages•
Advantages$and$Disadvantages:$Raster
Raster/Vector$Conversion
Vector$to$raster$conversoin
○
Smooth$lines$become$jagged
○
Areas$smaller$than$pixel$size$disappear
○
Mixed$pixel$problem
○
Rasterization•
Raster$to$vector$conversion
○
Works$well$with$discrete$rasters,$not$so$well$for$continuous
○
Lines$are$straightened
○
Where$to$draw$the$lines$becomes$an$issue
○
Vectorization•
Conversions
Superimpose$grid•
Depending$on$rules$of$encoding,$assigns$definite$values$to$pixels$
○
Apply$rules$(majority,$where$data$touches$pixel)
○
Rules$applied
○
Increases$data$size
§
Can$solve$problems$with$shape$accuracy$by$reducing$grid$size
○
Assign$definite$values•
Vector$to$Raster
Week$3:$Data$Referencing
Tuesday,$ May$15,$2018
8:55$AM
How$are$Data$Represented$in$a$GIS?
Data$model:$set$of$constructs$for$representing$the$"real$world"$in$the$digital$
environment$of$a$GIS
•
Geography$is$represented$as$either$objects(or(fields•
Objects,$Fields$and$Data$Models
Discrete$entities;$well-defined$boundaries•
Recognizable$classes•
Countable•
0-dimensional
○
1-dimensional$lines
○
2-dimensional$areas$(polygons)
○
Dimensionally$defines$three$primitives•
Objects
Variables$change$in$value$at$all$locations
○
Continuous$surface•
Values$that$exist$virtually$everywhere•
Ex.$Soil$properties,$elevation,$precipitation•
Fields
Vector$Representation:$what$each$colour$represents$(dark$green=$forest,$
blue=water,$
•
Raster:$defined$by$pixels;$pixelated;$not$as$clean$boundaries$potentially•
Elevation:$contour$lines=vector,$pixels=raster•
Land$use:$Raster=right•
Buildings:$Raster=$left•
Representation$Examples
Vector$Data$Model
Represents$discrete$objects•
Vectors$better$for$defining$boundaries$more$precisely
§
Precise$nature$of$its$representation$method
○
Quality$of$cartographic$output
○
Only$tells$you$"what$is$where"
§
Raster$tells$you$"what$is$everywhere"$;$even$if$nothing$there,$a$pixel$
represents$that$data
§
Storage$efficiency
○
Topology
○
Widely$implemented•
Space$defined$by$continuous$XY$coordinates
•
Object$locations$defined$by$XY$coordinate$pairs
•
Coordinate$pairs$are$used$as$building$blocks$for$more$complex$features;$lines$
and$polygons
•
Vector$Representation
Point$data$set
•
Locating$specific$objects
•
Identifier$and$coordinate$pair$needed
•
Utility$companies:$mapping$
•
Points
Points$connected$together
•
One/several$segments=$arc
•
Endpoints$of$arc$are$nodes
•
Angle$points$are$vertices
•
Feature$starts$and$ends$with$a$node
○
Feature$is$defined$by$the$arc,$not$the$line
•
Two$arcs$meet$at$the$nodes
•
Lines
Perfectly$enclosed
•
Simple$polygon:$composed$with$lines$with$common$beginning/ending$node
•
Complex$polygon:$contains$"islands";$definition$of$"inside"$is$more$complex
•
Ex.$S.$Africa
•
Polygons
Topology
Mathematical$procedure$for$defining$spatial$relationships;$i.e.$mathematics$of$
connectivity$and$adjacency$for$spatial$features$(how$features$join)
•
Validate$geometry$of$vector$datasets$(check$to$see$polygons$are$closed,$
lines$are$connected,$etc.$
○
Various$operations$(spatial$search,$shortest$path,$etc)
○
Used$in$GIS:
•
If$topology$in$effect,$projections$do$not$alter$facts$(ex.$Continguous$$polygons)
•
Knows$where$it$is
○
Knows$what$is$around$it
○
Has$recognized$spatial$relationships$with$other$features
○
Has$length,$distance,$perimeter$and$area$information
○
Knows$how$to$get$around
○
Understands$its$environment
○
With$topology,$each$feature$has$the$following$characteristics
•
Can$be$used$to$identify$spatial$associations$between$or$among$geographic$
features
•
Containment;$something$within$something$else$(counties$have$to$be$
within$province)
○
Adjacency/proximity
○
Connectivity
○
Intersection/overlap
○
Types$of$spatial$association•
How$do$spatial$patterns$and$distributions$of$volcanoes$relate$to$location$
of$tectonic$boundaries
○
Topology$helps$us$see$that
○
Proximity•
Overpass$vs.$intersection$represented$with$nodes$or$not
○
Interchanges$for$highways;$what$is$actually$intersecting$vs.$overpasses
○
Intersection$and$overlap•
Topology
How$we$create$topology•
Representation$of$vector$objects$in$computer•
Vector$Encoding
Bunch$of$overlapping$lines
○
Simple$structure
○
List$of$coordinates,$with$lots$of$duplication$particularly$in$polygon$data$
sets
○
Each$feature$has$no$knowledge$of$other$features$that$it$intersects,$
is$adjacent$to,$contiguous$with$or$near
§
No$relative$relationships$encoded$in$this$model
○
Generally$come$from$CAD$files
○
Non-topological$data$model•
Spaghetti$Data$Model
"arc-node$model"•
Points=$lowercase$letters$(blue$and$green)•
Arrows$showing$direction$of$encoding•
Done$feature$by$feature:$•
Topological$Data$Model
XY$coordinate$for$each$point•
Node$File
From-node,$To-node,$vertices,$Left$polygon,$Right$polygon$(polygons$oriented$
based$on$direction$of$encoding)
•
Blue=nodes,$green=vertices•
*Defined$by$system*•
Coverage:$topological$data$structure$(folder);$where$you$find$table$of$Arc$info$
(.aat)
•
Shapefiles:$non-topological$structure;$series$of$connected$arcs,$polygons$or$
points
•
Geodatabase:$topological;$based$on$common$language$rules;$putting$topological$
data$into$semantic$language$
•
Arc$File
Identifier$for$polygon$and$arcs$that$make$up$polygons•
"0"$indicates$what$follows$is$within$polygon•
Polygon$File
Shapefiles,$coverages
§
Spatial$and$attribute$data
§
Geo-spatial$part
§
Relational-database$part
§
Classical$approach$to$vector$data
§
Georelational$
○
Spatial$and$tabular$components$are$stored$in$single$system
§
Spatial$features$can$have$properties$and$methods
§
Recent$trends$towards$object-based$models
§
Specific$behaviours$modelled
§
Object-based
○
Two$Common$Methods•
Storing$Vector$Data
Raster$Data$Model
R$data$model$used$to$represent$both$fields$and$objects•
Degree$of$generalization$for$linear$features$depends$on$pixel$sizes•
Divides$space$into$series$of$units$(grid$cells)
○
Each$unit$same$in$size
○
Cellular$organization•
Every$pixel$ needs$a$value
○
JPEG,$GIF,$BMP,$and$TIF$are$raster$formats
○
Each$pixel$ encoded$with$specific$value•
Used$to$represent$digital$orthophotos,$DEMS,$categorical$data,$multispectral$
images,$etc
•
Raster$Representation
Assigned$one$value$only•
How$do$you$assign$values$to$cells$containing$more$than$one$feature
○
Mixed$pixel$problem:•
Value$of$a$cell$may$be$based$on$a$domination$scheme,$the$commonest$
value$in$the$cell,$or$the$edge$itself
○
May$also$be$the$value$found$at$the$cell's$central$point
○
Assignment$scheme•
Cell$Values
Values$are$integers•
Refers$to$limited$number$of$classes•
Pixels$with$same$value$equals$same$class•
Similar$to$polygons•
Ex.$Soild$class,$vegetation$class•
Discrete$Raster
Any$values$within$a$range
○
decimals
○
Values$are$floating$point•
Also$called$surface•
Digital$elevation$model
○
Ex.$Elevation,$precipitation,$air$pollution•
Continuous$Raster
If$projected,$origin$is$bottom$left
§
Origin$of$raster$is$upper$left$corner$(unprojected)
○
Not$stored$as$XY;$cell$has$an$implied$location;$only$grid$origin$is$stored•
Locational$precision$is$based$on$cell$size•
Cell$location$refers$to$center$of$cell•
Locational$Precision
Size$of$grid$cell$ or$picture$element,$defining$level$of$spatial$detail$in$
ground$units
○
Pixel$size=$Minimum$Mapping$Unit=$$resolution
○
Variation$within$pixels$is$lost;$coarser$the$resolution$the$less$variation
○
Resolution$(pixel$size)•
Increase$detail$by$decreasing$pixel$size•
Can$effectively$replicate$ vector$structures$with$small$enough$grid$cell$sizes•
Level$of$detail$required
○
Features$being$mapped
○
Storage$available$and$machine$speed
○
Decision$based$on:•
Tradeoff$between$detail$and$storage•
Resolution
1/2$pixel$width=$4x$data$volume•
Lots$of$variability=$need$smaller$pixels•
Data$Volume
No$compression
○
Just$a$line-scan
○
"AAAAABBBAABBAAAB"
○
Worst$case
○
Sequential$encoding•
Everything$along$a$line
○
Scans$across$rows
○
If$identical$pixels,$represented$by$number$of$consecutive$pixels
○
Each$row$separated
○
Ex.$First$row$has$7$A's$in$a$row:$7A
○
Run$length•
Cuts$across$different$rows
○
If$identical$throughout$rows,$represented$by$number$of$consecutive$rows
○
Continuous$zig-zag$pattern
○
Row$order•
Cuts$across$rows,$follows$down$to$next$row$vertically
○
Not$a$zig$zag$pattern
○
Row$prime$order•
Example•
AAAA
A B B B
A A B B
AAAB
AAAAABBBAABBAAAB
○
Sequential$(16)•
4A$1A$3B$2A$2B$3A$1B
○
Run$Length$(14)•
5A$3B$2A$2B$3A$1B
○
Run$Length-Row$Order$(12)•
4A$3B$3A$3B$3A$(top$left)
○
5A$5B$5A$1B$(top$right)
○
Run$Length-Row$Prime$Order$(10$or$8)•
Data$Compression
Uses$cells$of$different$sizes$depending$upon$information$density•
Large$cells$in$smooth$areas,$small$ones$in$highly$variable$areas•
More$efficient$storage$than$run-length$encoding•
Makes$display$analysis$faster•
Quadtree$Data$Model
Divide$into$4$quadrants
○
If$quadrant$is$homogenous$then$leave$as$is
○
A$quadrant$is$homogenous
§
OR
Highest$level$ of$resolution$is$reached
§
Otherwise,$recursively$subdivide$until
○
Summary:•
Building$a$Quadtree
Root$into$Leaf$into$Node•
If$odd$number$of$rows$or$columns,$system$will$add$blank$"no$data"$row$and$
column$to$be$able$to$divide$evenly
•
Quadtree$Organization
Raster$vs.$Vector
Point•
Simple$line•
Complex$line•
Single$polygon•
Connected$polygons•
Raster$and$Vector$Data$Structure
If$discrete,$vector$the$better$one
§
Discreteness$of$entity$being$depicted
○
Certain$only$applicable$by$one$or$the$other
§
Ex.$Road$networks$and$shortest$path:$vector$better$
§
Intended$applications
○
Vector$based$map$(road$map)
§
Source$data
○
Vector$data$is$smaller,$compact$(especially$in$.gdb)
§
Raster$has$to$tell$us$everything$in$study$area,$even$if$not$relevant;$
files$considerably$larger
§
Storage$considerations
○
Must$consider•
Considerations
Good$representation$of$reality
○
More$efficient$data$storage
○
Topology$can$be$described$as$network
○
Accurate$graphics
○
Variety$of$attributes$can$be$associated$with$one$feature
○
Feature$based$processing
○
Advantages•
Complex$data$structures
○
Simulation$may$be$difficult
○
Some$spatial$analysis$operations$are$difficult$or$impossible$to$perform
○
Disadvantages•
Advantages$and$Disadvantages:$Vector
Easy$overlay
○
Simple$data$structure,$geographic$position$is$implicit
○
Various$kinds$of$spatial$analysis$available
○
Uniform$size$and$shape
○
Can$accommodate$both$discrete$and$continuous$features
○
Compatible$with$remotely$sensed$data
○
Advantages•
Large$amount$of$data
○
Less$"pretty"
○
Projection$transformation$is$more$difficult
○
Different$resolutions$between$layers$may$be$a$nightmare
○
May$lose$information$due$to$generalization
○
Disadvantages•
Advantages$and$Disadvantages:$Raster
Raster/Vector$Conversion
Vector$to$raster$conversoin
○
Smooth$lines$become$jagged
○
Areas$smaller$than$pixel$size$disappear
○
Mixed$pixel$problem
○
Rasterization•
Raster$to$vector$conversion
○
Works$well$with$discrete$rasters,$not$so$well$for$continuous
○
Lines$are$straightened
○
Where$to$draw$the$lines$becomes$an$issue
○
Vectorization•
Conversions
Superimpose$grid•
Depending$on$rules$of$encoding,$assigns$definite$values$to$pixels$
○
Apply$rules$(majority,$where$data$touches$pixel)
○
Rules$applied
○
Increases$data$size
§
Can$solve$problems$with$shape$accuracy$by$reducing$grid$size
○
Assign$definite$values•
Vector$to$Raster
Week$3:$Data$Referencing
Tuesday,$ May$15,$2018 8:55$AM
How$are$Data$Represented$in$a$GIS?
Data$model:$set$of$constructs$for$representing$the$"real$world"$in$the$digital$
environment$of$a$GIS
•
Geography$is$represented$as$either$objects(or(fields•
Objects,$Fields$and$Data$Models
Discrete$entities;$well-defined$boundaries•
Recognizable$classes•
Countable•
0-dimensional
○
1-dimensional$lines
○
2-dimensional$areas$(polygons)
○
Dimensionally$defines$three$primitives•
Objects
Variables$change$in$value$at$all$locations
○
Continuous$surface•
Values$that$exist$virtually$everywhere•
Ex.$Soil$properties,$elevation,$precipitation•
Fields
Vector$Representation:$what$each$colour$represents$(dark$green=$forest,$
blue=water,$
•
Raster:$defined$by$pixels;$pixelated;$not$as$clean$boundaries$potentially•
Elevation:$contour$lines=vector,$pixels=raster•
Land$use:$Raster=right•
Buildings:$Raster=$left•
Representation$Examples
Vector$Data$Model
Represents$discrete$objects•
Vectors$better$for$defining$boundaries$more$precisely
§
Precise$nature$of$its$representation$method
○
Quality$of$cartographic$output
○
Only$tells$you$"what$is$where"
§
Raster$tells$you$"what$is$everywhere"$;$even$if$nothing$there,$a$pixel$
represents$that$data
§
Storage$efficiency
○
Topology
○
Widely$implemented•
Space$defined$by$continuous$XY$coordinates•
Object$locations$defined$by$XY$coordinate$pairs•
Coordinate$pairs$are$used$as$building$blocks$for$more$complex$features;$lines$
and$polygons
•
Vector$Representation
Point$data$set•
Locating$specific$objects•
Identifier$and$coordinate$pair$needed•
Utility$companies:$mapping$•
Points
Points$connected$together•
One/several$segments=$arc•
Endpoints$of$arc$are$nodes•
Angle$points$are$vertices•
Feature$starts$and$ends$with$a$node
○
Feature$is$defined$by$the$arc,$not$the$line•
Two$arcs$meet$at$the$nodes•
Lines
Perfectly$enclosed•
Simple$polygon:$composed$with$lines$with$common$beginning/ending$node•
Complex$polygon:$contains$"islands";$definition$of$"inside"$is$more$complex•
Ex.$S.$Africa•
Polygons
Topology
Mathematical$procedure$for$defining$spatial$relationships;$i.e.$mathematics$of$
connectivity$and$adjacency$for$spatial$features$(how$features$join)
•
Validate$geometry$of$vector$datasets$(check$to$see$polygons$are$closed,$
lines$are$connected,$etc.$
○
Various$operations$(spatial$search,$shortest$path,$etc)
○
Used$in$GIS:•
If$topology$in$effect,$projections$do$not$alter$facts$(ex.$Continguous$$polygons)•
Knows$where$it$is
○
Knows$what$is$around$it
○
Has$recognized$spatial$relationships$with$other$features
○
Has$length,$distance,$perimeter$and$area$information
○
Knows$how$to$get$around
○
Understands$its$environment
○
With$topology,$each$feature$has$the$following$characteristics•
Can$be$used$to$identify$spatial$associations$between$or$among$geographic$
features
•
Containment;$something$within$something$else$(counties$have$to$be$
within$province)
○
Adjacency/proximity
○
Connectivity
○
Intersection/overlap
○
Types$of$spatial$association
•
How$do$spatial$patterns$and$distributions$of$volcanoes$relate$to$location$
of$tectonic$boundaries
○
Topology$helps$us$see$that
○
Proximity
•
Overpass$vs.$intersection$represented$with$nodes$or$not
○
Interchanges$for$highways;$what$is$actually$intersecting$vs.$overpasses
○
Intersection$and$overlap
•
Topology
How$we$create$topology
•
Representation$of$vector$objects$in$computer
•
Vector$Encoding
Bunch$of$overlapping$lines
○
Simple$structure
○
List$of$coordinates,$with$lots$of$duplication$particularly$in$polygon$data$
sets
○
Each$feature$has$no$knowledge$of$other$features$that$it$intersects,$
is$adjacent$to,$contiguous$with$or$near
§
No$relative$relationships$encoded$in$this$model
○
Generally$come$from$CAD$files
○
Non-topological$data$model
•
Spaghetti$Data$Model
"arc-node$model"
•
Points=$lowercase$letters$(blue$and$green)
•
Arrows$showing$direction$of$encoding
•
Done$feature$by$feature:$
•
Topological$Data$Model
XY$coordinate$for$each$point•
Node$File
From-node,$To-node,$vertices,$Left$polygon,$Right$polygon$(polygons$oriented$
based$on$direction$of$encoding)
•
Blue=nodes,$green=vertices•
*Defined$by$system*•
Coverage:$topological$data$structure$(folder);$where$you$find$table$of$Arc$info$
(.aat)
•
Shapefiles:$non-topological$structure;$series$of$connected$arcs,$polygons$or$
points
•
Geodatabase:$topological;$based$on$common$language$rules;$putting$topological$
data$into$semantic$language$
•
Arc$File
Identifier$for$polygon$and$arcs$that$make$up$polygons•
"0"$indicates$what$follows$is$within$polygon•
Polygon$File
Shapefiles,$coverages
§
Spatial$and$attribute$data
§
Geo-spatial$part
§
Relational-database$part
§
Classical$approach$to$vector$data
§
Georelational$
○
Spatial$and$tabular$components$are$stored$in$single$system
§
Spatial$features$can$have$properties$and$methods
§
Recent$trends$towards$object-based$models
§
Specific$behaviours$modelled
§
Object-based
○
Two$Common$Methods•
Storing$Vector$Data
Raster$Data$Model
R$data$model$used$to$represent$both$fields$and$objects•
Degree$of$generalization$for$linear$features$depends$on$pixel$sizes•
Divides$space$into$series$of$units$(grid$cells)
○
Each$unit$same$in$size
○
Cellular$organization•
Every$pixel$ needs$a$value
○
JPEG,$GIF,$BMP,$and$TIF$are$raster$formats
○
Each$pixel$ encoded$with$specific$value•
Used$to$represent$digital$orthophotos,$DEMS,$categorical$data,$multispectral$
images,$etc
•
Raster$Representation
Assigned$one$value$only•
How$do$you$assign$values$to$cells$containing$more$than$one$feature
○
Mixed$pixel$problem:•
Value$of$a$cell$may$be$based$on$a$domination$scheme,$the$commonest$
value$in$the$cell,$or$the$edge$itself
○
May$also$be$the$value$found$at$the$cell's$central$point
○
Assignment$scheme•
Cell$Values
Values$are$integers•
Refers$to$limited$number$of$classes•
Pixels$with$same$value$equals$same$class•
Similar$to$polygons•
Ex.$Soild$class,$vegetation$class•
Discrete$Raster
Any$values$within$a$range
○
decimals
○
Values$are$floating$point•
Also$called$surface•
Digital$elevation$model
○
Ex.$Elevation,$precipitation,$air$pollution•
Continuous$Raster
If$projected,$origin$is$bottom$left
§
Origin$of$raster$is$upper$left$corner$(unprojected)
○
Not$stored$as$XY;$cell$has$an$implied$location;$only$grid$origin$is$stored•
Locational$precision$is$based$on$cell$size•
Cell$location$refers$to$center$of$cell•
Locational$Precision
Size$of$grid$cell$ or$picture$element,$defining$level$of$spatial$detail$in$
ground$units
○
Pixel$size=$Minimum$Mapping$Unit=$$resolution
○
Variation$within$pixels$is$lost;$coarser$the$resolution$the$less$variation
○
Resolution$(pixel$size)•
Increase$detail$by$decreasing$pixel$size•
Can$effectively$replicate$ vector$structures$with$small$enough$grid$cell$sizes•
Level$of$detail$required
○
Features$being$mapped
○
Storage$available$and$machine$speed
○
Decision$based$on:•
Tradeoff$between$detail$and$storage•
Resolution
1/2$pixel$width=$4x$data$volume•
Lots$of$variability=$need$smaller$pixels•
Data$Volume
No$compression
○
Just$a$line-scan
○
"AAAAABBBAABBAAAB"
○
Worst$case
○
Sequential$encoding•
Everything$along$a$line
○
Scans$across$rows
○
If$identical$pixels,$represented$by$number$of$consecutive$pixels
○
Each$row$separated
○
Ex.$First$row$has$7$A's$in$a$row:$7A
○
Run$length•
Cuts$across$different$rows
○
If$identical$throughout$rows,$represented$by$number$of$consecutive$rows
○
Continuous$zig-zag$pattern
○
Row$order•
Cuts$across$rows,$follows$down$to$next$row$vertically
○
Not$a$zig$zag$pattern
○
Row$prime$order•
Example•
AAAA
A B B B
A A B B
AAAB
AAAAABBBAABBAAAB
○
Sequential$(16)•
4A$1A$3B$2A$2B$3A$1B
○
Run$Length$(14)•
5A$3B$2A$2B$3A$1B
○
Run$Length-Row$Order$(12)•
4A$3B$3A$3B$3A$(top$left)
○
5A$5B$5A$1B$(top$right)
○
Run$Length-Row$Prime$Order$(10$or$8)•
Data$Compression
Uses$cells$of$different$sizes$depending$upon$information$density•
Large$cells$in$smooth$areas,$small$ones$in$highly$variable$areas•
More$efficient$storage$than$run-length$encoding•
Makes$display$analysis$faster•
Quadtree$Data$Model
Divide$into$4$quadrants
○
If$quadrant$is$homogenous$then$leave$as$is
○
A$quadrant$is$homogenous
§
OR
Highest$level$ of$resolution$is$reached
§
Otherwise,$recursively$subdivide$until
○
Summary:•
Building$a$Quadtree
Root$into$Leaf$into$Node•
If$odd$number$of$rows$or$columns,$system$will$add$blank$"no$data"$row$and$
column$to$be$able$to$divide$evenly
•
Quadtree$Organization
Raster$vs.$Vector
Point•
Simple$line•
Complex$line•
Single$polygon•
Connected$polygons•
Raster$and$Vector$Data$Structure
If$discrete,$vector$the$better$one
§
Discreteness$of$entity$being$depicted
○
Certain$only$applicable$by$one$or$the$other
§
Ex.$Road$networks$and$shortest$path:$vector$better$
§
Intended$applications
○
Vector$based$map$(road$map)
§
Source$data
○
Vector$data$is$smaller,$compact$(especially$in$.gdb)
§
Raster$has$to$tell$us$everything$in$study$area,$even$if$not$relevant;$
files$considerably$larger
§
Storage$considerations
○
Must$consider•
Considerations
Good$representation$of$reality
○
More$efficient$data$storage
○
Topology$can$be$described$as$network
○
Accurate$graphics
○
Variety$of$attributes$can$be$associated$with$one$feature
○
Feature$based$processing
○
Advantages•
Complex$data$structures
○
Simulation$may$be$difficult
○
Some$spatial$analysis$operations$are$difficult$or$impossible$to$perform
○
Disadvantages•
Advantages$and$Disadvantages:$Vector
Easy$overlay
○
Simple$data$structure,$geographic$position$is$implicit
○
Various$kinds$of$spatial$analysis$available
○
Uniform$size$and$shape
○
Can$accommodate$both$discrete$and$continuous$features
○
Compatible$with$remotely$sensed$data
○
Advantages•
Large$amount$of$data
○
Less$"pretty"
○
Projection$transformation$is$more$difficult
○
Different$resolutions$between$layers$may$be$a$nightmare
○
May$lose$information$due$to$generalization
○
Disadvantages•
Advantages$and$Disadvantages:$Raster
Raster/Vector$Conversion
Vector$to$raster$conversoin
○
Smooth$lines$become$jagged
○
Areas$smaller$than$pixel$size$disappear
○
Mixed$pixel$problem
○
Rasterization•
Raster$to$vector$conversion
○
Works$well$with$discrete$rasters,$not$so$well$for$continuous
○
Lines$are$straightened
○
Where$to$draw$the$lines$becomes$an$issue
○
Vectorization•
Conversions
Superimpose$grid•
Depending$on$rules$of$encoding,$assigns$definite$values$to$pixels$
○
Apply$rules$(majority,$where$data$touches$pixel)
○
Rules$applied
○
Increases$data$size
§
Can$solve$problems$with$shape$accuracy$by$reducing$grid$size
○
Assign$definite$values•
Vector$to$Raster
Week$3:$Data$Referencing
Tuesday,$ May$15,$2018 8:55$AM
