layers in a raster model

layers in a raster model Layer 1 Layer 2

layers in an vector-based model (1) Layer 2 Layer 1

layers in an vector-based model (2)

raster versus vector data model Raster model Vector model Simple data structure Easy and efficient overlaying Compatible with Remote Sensing imagery High spatial variability is efficiently represented Simple for programming by user Same grid cell definition for various attributes Inefficient use of computer storage Errors in perimeter and shape Difficult to perform network analysis Inefficient projection transformations Loss of information when using large pixel sizes Less accurate and less appealing map output Complex data structure Difficult to perform overlaying Not compatible with RS imagery Inefficient representation of high spatial variability Compact data structure Efficient encoding of topology Easy to perform network analysis Highly accurate map output

Quadtree data structure In this, geographical area is decomposed into four quadrants and the decomposition continues until each quad represents a homogenous unit. The storage requirement of a quadree is much lower than that of a raster having the resolution of the smallest quad element

Quadtree data structure In this, geographical area is decomposed into four quadrants and the decomposition continues until each quad represents a homogenous unit. The storage requirement of a quadtree is much lower than that of a raster having the resolution of the smallest quad element

THE QUADTREE DATA STRUCTURE WORKS WITH: LEVELS QUADRANTS HOMOGENEOUS AREAS

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Quad trees advantages : - computation of standard region properties is easy - variable resolution and hence less storage requirement disadvantages : - translation invariant (two regions having same size and shape can produce different quadtrees. - cannot split into parts

Course Content Introduction to GIS, Definitions of GIS and Overview, History and concepts of GIS, Development of GIS, Scope and application areas Geographical Entities, Attribute data, Linking spatial and attribute data Spatial Data Models, raster vs vector, Raster data Models, Spatial Relationships, GIS Data Analysis, Raster data analysis tools Mapping concepts, Map elements, Map scales and representation, Map projections and coordinate systems Practical and Case Studies Laboratory Sessions: Introduction to Arc GIS, Strength of Arc GIS, Some hands-on session in introducing the ARC GIS environment

Feature relationships & Topology There are vast number of possible relationships in spatial data. Relationships are important in GIS analysis. "is contained in" relationship between a point and an area is important in relating objects to their surrounding environment. "intersects" between two lines is important in analyzing routes through networks Relationships can exist between entities of the same type or of different types. for each shopping center, can find the nearest shopping center (same type) for each customer, can find the nearest shopping center (different types)

Types of relationship Relationships which are used to construct complex objects from simple primitives. Relationship between a line and the ordered set of points which defines it. Relationship between a polygon and the ordered set of lines which defines it. Relationships which can be computed from the coordinates of the objects. Areas can be examined to see which one encloses a given point - the "is contained in" relationship can be computed. Areas can be examined to see if they overlap - the "overlaps" relationship. Relationships which cannot be computed from coordinates We can compute if two lines cross, but not if the highways they represent intersect (may be an overpass). Objects representing "house", "lot", plot", with associated attributes might be grouped together logically as sellers account.

Spatial relationships Point-point "is within", e.g. find all of the customer points within 1 km of this retail store point "is nearest to", e.g. find the hazardous waste site which is nearest to this groundwater well Point-line "ends at", e.g. find the intersection at the end of this street "is nearest to", e.g. find the road nearest to this aircraft crash site Point-area "is contained in", e.g. find all of the customers located in this ZIP code boundary "can be seen from", e.g. determine if any of this lake can be seen from this viewpoint

Spatial relationships Line-line "crosses", e.g. determine if this road crosses this river "comes within", e.g. find all of the roads which come within 1 km of this railroad "flows into", e.g. find out if this stream flows into this river Line-area "crosses", e.g. find all of the soil types crossed by this railroad "borders", e.g. find out if this road forms part of the boundary of this airfield Area-area "overlaps", e.g. identify all overlaps between types of soil on this map and types of land use on this other map "is nearest to", e.g. find the nearest lake to this forest fire "is adjacent to", e.g. find out if these two areas share a common boundary

Relationships as attributes Example: Flows-in relationship Option A Link ID 001 004 002 004 003 005 004 005 005 empty Downstream 003 001 004 005 002 Each stream link in a stream network could be given the ID of the downstream link which it flows into Flow could be traced from link to link by following pointers Option B Link ID Pointer 001 0001 002 0001 003 0002 004 0002 005 empty Point ID 0001 0002 Pointer 0001 004 0002 005 Each stream link in a stream network could be given the ID of the downstream point which it flows into Each stream point in a stream network could be given the ID of the downstream link which it flows into Flow could be traced from link to link by following pointers

Relationships as attributes Example: is contained in relationship 1. Find the containing county of each well (compute the is contained in relationship). 2. Store the result as a new attribute, County, of each well. 3. Using this revised attribute table, total flow by county and add results to the county table. Well ID County A 001 A 002 B 003 A 004 A 001 004 002 003 County County B County ID A 3 B 1 No. of Wells

Object Pairs Some attribute is between a pair of objects. Distance is the attribute of a pair of objects. Flow of commuters between two places. Trade between two counties. In some cases these attributes can be attached to an object linking the origin and destination objects. For example, trade can be attached to an arrow pointing from county A to B. In general, these kind of attributes shall be described using separate tables or matrix. A C B D A B C D A 0 1 1.5 2.5 B 1 0 1 2 C 1.5 1 0 3 D 2.5 2 2.5 0 A distance table between points A, B, C, and D

Topology Topology is a branch of mathematics that deals with properties of space that remain invariant under certain transformations. Properties : 3 spatial relationships Containment: Polygons can be defined by set of lines enclose them Contiguity: Identification of polygons which touch each other or connect identify contiguous polygons (left or right) Connectivity: Identification of interconnected arcs, starting point & end point of network analysis

GIS topology Topology is a mathematics approach that defines unchangeable spatial relationships. When a map is stretched or distorted, some properties change, Distance Angles Relative proximities Some properties won t change, Adjacencies Most other relationships, such as "is contained in", "crosses" Types of spatial objects - areas remain areas, lines remain lines, points remain points These unchanged properties are called topological properties.

Topological examples Network connectivity Polygon adjacency Topology poorly-defined Topology well-defined

Importance of topology Topology enables operations like connectivity and contiguity analysis. Searching a shortest path Finding a service area by using a road network Finding adjacent areas Topology enables spatial analysis without using a coordinate set, Apply spatial analysis using topological definitions alone Major difference from CAD or computer-aided cartography

Topology and GIS analysis Searching a shortest path Finding adjacent areas 1 2 3 2 2.5 2 2.5 2 The shortest path from the blue point to the yellow point is through the red point and then the orange point (2+1+2.5=5.5 map units). However, if the topology of the red point is not defined clearly, which means the two purple lines are consider as one and the two orange lines are considered as one, the resulting answer will be wrong (2+2+2=6 map units). The overlapped two polygons have to be cut into three in order to clearly defined the spatial topology. Otherwise there will be difficulties finding an adjacent polygon of either.

Editing coincident features The spatial relationship between two polygon features is distorted when edited incorrectly. The primary purpose of a topology is to define spatial relationships between features. The primary spatial relationships that you can model using topology are adjacency (contiguity), coincidence (containment) and connectivity. When editing features, it's important to maintain the spatial relationships that exist among them. For example, when you edit the shared boundary between two land use features, you don't want to introduce a gap between the two. To prevent editing errors, you can create a topology.

Topological Consistency Relations Every line is bounded by two points. For every line there are two adjacent areas (left and right polygon). Every area (polygon) is bounded by a closed cycle of points and lines. Every point is surrounded by a closed cycle of lines and areas. Lines intersect only in points.

Topological Invariants Exterior Interior Boundary

Topological Relationships Relationships between two regions can be determined based on the intersection of their boundaries and interiors (4-intersection). A B

Lines: fundamental spatial data model node vertex vertex node vertex vertex Lines start and end at nodes line #1 goes from node #2 to node #1 Vertices determine shape of line Nodes and vertices are stored as coordinate pairs

Polygons: fundamental spatial data model Polygon #2 is bounded by lines 1 & 2 Line 2 has polygon 1 on left and polygon 2 on right

Polygons: fundamental spatial data model complex data model, especially for larger data sets arc-node topology, used for ArcInfo data sets or defined by rules in the Geodatabase.

Spatial Relationships disjoint covered by meet contains equal covers inside overlap

Spatial Relationships Between Geometries Boolean operators Adjacency - Intersect Coincidence - Touch Connectivity- Disjointness Equal the same Disjoint contain a common point Intersect cut each other Touch at boundaries Cross overlap (different dimensions) Within is one within another Contain completely within another Overlap (same dimension) Relate are intersections between the interior, boundary, or exterior of boundaries

Feature Geometry Geometry and Features Points and Multipoints Polylines Polygons Envelopes

Geometry and Features Components of Feature Geometries Rings Segments Paths Attributes of Feature Geometries Vertical measurements with z values Linear measurements with m values

Testing Spatial Relationships Equals Contains

Testing Spatial Relationships Within Crosses

Testing Spatial Relationships Overlaps Disjoint Touches

Applying Topological Operators Buffer Clip Convex Hull Cut

Applying Topological Operators Difference Intersect Symmetric Difference Union

Define an area where spotted owls have been spotted Convex Hull Create a convex hull for data set the smallest convex polygon that contains the set of points

(Raster based) overlay operation tools Arithmetic functions (+, -, *, /) Relational functions (<, >, =) Logical operations (and, or, xor, not) Conditional functions ( if, then, else )

Logical functions Boolean operators A AND B = A B intersection A OR B = A B union A XOR B = A B exclusion A NOT B = A B negation

Arithmetic operations 5 5 5 5 6 4 4 8 4 4 4 1 Map A Map B 1 1 1 5 2 2 2 2 1 2 2 6 6 6 6 8 8 8 8 8 MapC= MapA + 10 Map C 15 15 12 12 15 15 15 12 16 12 12 12 16 16 16 16 MapC1= MapA + MapB Map C1 9 9 10 10 9 9 9 10 7 3 3 10 7 7 14 14 MapC2= ((MapA - MapB)/(MapA + MapB)) *100 Map C2 - - - - - - 11 11 60 11 11 11 71 33 33 60 60 60 71 71 14 14

Relational functions 5 5 5 5 6 4 4 8 4 4 4 1 Map A 1 1 1 5 2 2 2 2 Map B 1 2 2 6 6 6 6 8 8 8 8 8 Output = MAP A > MAP B 1 1 Output 1 1 1 1 1 1 1 0 1 0 0 = FALSE 1 = TRUE 0 0 0 0

Relational and logical operators F = forest 7 = 700 m 6 = 600 m 4 = 400 m MapD=(MapA= Forest ) and (MapB <500) MapD1=(MapA= Forest ) or (MapB <500) MapD2=(MapA= Forest ) xor (MapB <500) MapD3=(MapA= Forest ) and not (MapB <500) 7 7 7 7 7 4 F F F F 7 4 6 6 F F 7 4 4 F F 7 4 4 F F 4 4 4 4 6 6 6 6 6 F F F 0 0 0 0 0 0 0 0 0 0 0 0 Map D 1 1 0 1 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 Map D2 1 0 0 0 1 0 = false 1 = true 1 0 1 1 Map D1 1 1 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 0 0 0 1 1 Map D3 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1

Conditional functions Map C F F F F F MapC= iff(mapa= Forest,1,?) 1 1 1 1 1????? F F F? 1 1? 1 F F F?? 1 1 1 F F??? 1 1 7 7 7 7 4 7 7 7 7 4 4 4 4 4 4 6 6 4 4 4 6 6 6 6 6 MapC1=iff((MapA= Forest ) F = forest 7 = 700 m 6 = 600 m 4 = 400 m and (MapB= 700),1,0) 1 1 Map C1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = false 1 = true? = undefined 0 0 0 0 0 0

Overlaying using and statement Landuse = forest AND Slope = steep