UNC at Chapel Hill, Gregory Taff Geography 70 Spatial Data Models and Structure 11/18/2018 UNC at Chapel Hill, Gregory Taff

Representing the Real World Map Since GIS is based on the model of a map, we have covered elements of maps up to this point. If you remember back a few lectures, I said that the three elements of a map are scale, projection and symbolization. We’ve talked about scale. We’ve covered projection and the elements that go along with it: geodesy and coordinate systems Now, we come to symbolization. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Symbolization In a GIS, we represent real world phenomena in a digital format 1 0 0 1 0 0 1 1 1 1 1 0 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Vocabulary Entity Data objects 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Terminology Entity -- a real world phenomenon to be represented in a database There are some terms that you need to know that help describe how this real world-to-digital data conversion takes place. Real world phenomena are known as entities. Some entities might be: Buildings Forest Roads Coastline Pastures Pasture boundaries Entities are the geographic objects in the real world that we want to represent in the GIS. Now keep in mind, like I’ve talked about before, there are two components to geographic data: location and attributes. We may create a representation of this road by drawing a line and assigning real world coordinates to it. However, there are features, information, attributes of the road that also need to be assigned. Speed limit and surface type may be important attributes. Keep this in mind as I go along here. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Terminology Data Object -- digital representation of an entity Pasture So you have your Entities, your real world objects that you want to put into the GIS. Entities are represented by Data Objects. A data object is… House Road 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Summary Data objects represent entities in a GIS. So to summarize, you have a data model that is made up of data objects, each of which represents a real world entity. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Topology The relationships between data objects in space. This relationship between objects in space, whether conceptually or logically, is known as topology. 11/18/2018 UNC at Chapel Hill, Gregory Taff

Conceptualizing Topology Adjacency Connectivity Containment Direction Proximity Overlap There are three primary components of topology. They are adjacency, connectivity and containment. There are also two other components that are important, but I consider them secondary components of topology. They are direction and proximity Can anybody give me a definition of adjacency? Just give it a shot. It’s not a special definition. How about connectivity? OK. What about containment? Direction is easy. Everyone knows where north is, right? Or do you? I’m going to do a quick test. I’m going to ask you which direction north is in from here. I will mention four landmarks around here. Everyone put your heads down. Now raise your hand if you think the Carolina Inn is north of here. Raise your hand if you think the Post Office downtown is north of here. Raise your hand if you think the Forest Theater is north. Raise your hand if you think Kenan Stadium is north. (Tally votes) See, not everyone inherently knows directions. When objects have a topological relationship, their direction in relation to each other can be determined. OK. Now, how about a definition of proximity. Good. Now, I’m going to go through these using an example that everyone should be familiar with. And I have to give credit where credit is due. John Spencer came up with these examples and I’m borrowing them from him. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Adjacency Springfield Shelbyville Adjacency – this relationship describes whether or not two objects are next to one another In this example, Springfield and Shelbyville are adjacent. In the real world, France and Germany are adjacent; France and England are not. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Connectivity Connectivity – are two objects connected? Here, Springfield is connected to South Springfield. Real World #1 (lines): Franklin St and Columbia are connected. They intersect. Real World #2 (areas): Chapel Hill and Raleigh are connected by I-40 Are they adjacent? No. But, Springfield and South Springfield are both connected and adjacent. So what is the difference, if any? Well, let’s take this adjacency vs. connectivity a step further. I may confuse you on this, but I just want to try and reinforce this idea. But it may only confuse you further. Think back to before the fall of the Berlin Wall. West Berlin and East Berlin were adjacent. But were they connected? Well, yes, there was a gate through the wall, but without the proper papers, you could not pass through it. So, for the majority of Berliners, the two cities were not connected. But they were definitely adjacent. Now, let’s think of England and France. They are definitely not adjacent. The English Channel separates them. But they are connected. We can say they are physically connected, because the Chunnel (the underwater tunnel) connects them. These roads are connected at the black points. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Containment Springfield Moe’s Kwik-E-Mart Connectivity – describes objects that may be wholly contained within an area Springfield contains Moe’s, the Kwik-E-Mart, and the Nuclear Plant Real World: University Lake is contained within the area of Orange County Nuclear Plant 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Direction Moe’s Kwik-E-Mart Nuclear Plant Moe’s is Northeast of the Kwik-E-Mart The nuclear plant is Southeast of the Kwik-E-Mart Direction. This is a human derived attribute. Direction is relative. Therefore, it is an important conceptual part of topology, but as you will see in a minute, it is not an important logical part of topology. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Proximity Homer lives near Ned Homer lives far from Grampa Proximity – how near certain objects are to each other, or far away from each other they are This is another relative measure. Once again, it is conceptual, not logical. It is also a derived measure. A GIS does not inherently know which objects are near each other. It is a subjective determination. Real Sesame Street kind of stuff, but they are important measures used in geography 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Overlap Blue Lake Springfield Adjacency – this relationship describes whether or not two objects are next to one another In this example, Springfield and Shelbyville are adjacent. In the real world, France and Germany are adjacent; France and England are not. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Review Topology The relationships between data objects in space. This relationship between objects in space, whether conceptually or logically, is known as topology. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff 2 GIS Data Models Entities in the real world are represented as one of the following in a GIS: Vector data: Points Lines Areas (or polygons) Raster data Pixels in an array Key concept! 11/18/2018 UNC at Chapel Hill, Gregory Taff

Raster data model (details later) The raster data model represents the Earth’s surface as a two-dimensional array of grid cells, with each cell having an associated value: 1 2 3 5 8 4 6 9 7 Cell (x,y) Cell value rows Cell size = resolution columns 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Raster data example Elevation data: each cell contains a number representing the elevation of that cell. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff The vector data model 11/18/2018 UNC at Chapel Hill, Gregory Taff

Vector Data Objects Geographic building blocks Points Lines Polygons 0 dimensional Lines 1 dimensional Polygons 2 dimensional The vector model is composed of three basic spatial objects, known as geographic primitives. They are known as this because they are the basis of geographic entities. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Spatial Objects Data objects in the vector data model can be: A point can represent: Tree, airport, a city, street intersection, a movie theater, a benchmark A line is a data object, made up of a connected sequence of points. It can represent: Roads, rivers, regional boundaries, fences, hedgerows, power lines A polygon is an enclosed area. Examples: A census tract, Saunders building, boundary of Chapel Hill, a lake, a watershed, a city 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Object example: oak tree 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Thought question: How are you going to represent the California OAK tree in digital format? A point? A polygon? Or a pixel? It will depend on: Scale of observation Purpose of your research The type of data you have access to in the GIS 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Thought questions: When do you want to represent Chapel Hill as a polygon object instead of a point object? When do you want to represent a river as a polygon instead of a line? 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff The vector data objects (x,y) (x,y) (x,y) (x,y) (x,y) (x,y) (x,y) (x,y) (x,y) (x,y) (x,y) point line polygon(area) The vector data model represents geographic features similar to the way maps do A point: recorded by a pair of (x,y) coordinates. A line: recorded by joining more than one point, A polygon: recorded by a joining multiple points that enclose an area 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Vector Data Storage in Computers: Points Data Storage Points Point ID Coordinates +4 1 1, 1 2 4, 2 3 6, 2 4 2, 4 +2 +3 +1 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Vector Data Storage in Computers: Lines (Sometimes called arcs) Line # Coordinates ① (x1, y1) (x2,y2) ② (x2,y2) (x3,y3) (x1,y1) (x2,y2) (x3,y3) ② ① Note: In GIS, this is considered a line (a connected set of individual lines). 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Vector Data Storage in Computers: Polygons Polygon # Coordinates ① (x1,y1) (x2,y2) (x3,y3) (x4,y4) ② (x3,y3) (x5,y5) (x6,y6) (x1,y1) (x2,y2) (x3,y3) (x4,y4) (x6,y6) (x5,y5) ① ② 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff The Arc-Node Data Structure Benefit: The arc-node structure allows efficient data storage for vector data How does it work? It stores data so that nodes construct arcs, and arcs construct polygons Nodes define the two endpoints of an arc. They may or may not connect two or more arcs. An arc is the line segment between two nodes. The points between two nodes defining the shape of an arc are called vertices. Nodes and vertices are represented as x, y coordinates. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff The Arc-Node Data Structure 2 3 Arc: ①, ②, ③ Nodes: 2, 5 Vertices: 1, 6 for arc ① 3, 4 for arc ② 1 ③ B ② A ① 4 5 6 Arc # Start Node Vertices End Node 2 1,6 5 2 3,4 5 2 5 Points 1 x1,y1 2 x2,y2 3 x3,y3 x4,y4 5 x5,y5 6 x6,y6 Polygon arc list A ①, ③ B ②, ③ 11/18/2018 UNC at Chapel Hill, Gregory Taff

Arc-Node Data Structure: enables Topology definition Topology defines spatial relationships. The arc-node data structure supports three major topological concepts: Connectivity: Arcs connect to each other at nodes Area definition: Arcs that connect to surround an area define a polygon Contiguity: Arcs have direction and left and right sides 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Topology: Connectivity Connected arcs are determined by searching through the list for common node numbers. Arc-node list 10 11 12 ① ② Arc From-Node To-Node 10 11 11 12 11 13 13 15 13 14 ③ ⑤ 13 14 ④ 15 Because of the common node 11, arcs 1, 2, and 3 all intersect. The computer can determine that it is possible to travel along arc 1 and turn onto arc 3. But it is not possible to turn directly from arc 1 to arc 5. 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Topology: Area Definition Polygon-Arc Topology 1 8 B Polygon Arc List B 1,5,8,4 C 2,6,9,5 D 6,3,4,7 E 9,7,8 5 C 4 2 E 9 D 6 7 3 Polygons are simply the list of arcs defining its boundary, arc coordinates are stored only once, therefore, reducing the amount of data and ensuring that the boundaries of adjacent polygons don’t overlap 11/18/2018 UNC at Chapel Hill, Gregory Taff

UNC at Chapel Hill, Gregory Taff Topology: Contiguity Two geographic features which share a boundary are called adjacent. Contiguity is the topological concept which allows the vector data model to determine adjacency. An Arc left From-Node To-Node right Direction 1 8 B Arc Left Right Polygon Polygon C B E C ? ? 1 ? ? 5 C 4 2 E 9 D 6 7 3 11/18/2018 UNC at Chapel Hill, Gregory Taff