MAPS AS NUMBERS

Outline

1. Image and Attribute Distinction
• Graphics verses Concepts
• Related to Mental Processing
• Importance of Language/Concepts
2. Vector
• Positive Quadrant of Cartesian Coordinate System
• Points, Lines, Areas
• Problems with Polygons
• Point Dictionary
• Arc/Node
3. Raster
• Grid Overlay
• Attributes Coded with Image
4. Other Forms of Coding

Image and Attribute Distinction

The graphic side of a map is the lines and descriptors. Examples of these lines are rivers or roads. Concepts, of human making, are the distinctions made between lines as being either a river or a road or land and water. The power of GIS is in linking the concepts or attributes and the graphic information in a useful way.

When visualizing a map the right and left sides of the brain are working at the same time. The right side of the brain is concentrating on the image and the left side is concentrating on the concept. The mental map would be the image side but the actual object (the river or the store) would be the concept.

Language is essential for attributes. The problem lies in the complexity of language because of its varying degrees of accuracy or classification. The classifying of the objects is part of the attribute side of a map. Everything is unique or different in some way; because of this classes of objects representative in the attributes must be created.

Vector

Vector is composed of points that represents an exact spatial coordinate. These points create lines that are broken down into a sequence of numbers that are stored in the computer's files. When laying out the coordinates for a point, line or area it is usually within the positive or first quadrant. This comes from the Cartesian Coordinate System. In this system the horizontal line is the "x" coordinate and the vertical line is the "y" coordinate. Maps are composed of lines of positive "x" and "y" coordinates.

A line has a certain vector or direction and is defined or composed of two x/y coordinates. An example of a point would be (3,4); in other words the point is located along the "x" coordinate at three and the "y" at four. A line has to be composed of at least two of these points (3,4), (6,8). Lines create polygons or the defined areas on the map. In Arcview the polygon format is called shapefile.

There are two main problems with polygons, both of which deal with adjoining polygons. When two polygons share a side or border the points along this side will be duplicated. The problem that arises from duplicating the points is the amount of data that has to be stored. The second problem is at the input stage. The digitizer can not get back to that same exact point. This creates gaps and overlays between the two polygons.

Point dictionary prevents duplication of points. It does this by labeling each point. It creates an array of numbers and in so doing decreasing the amount of data that must be stored.

The Arc/Node is another way to decrease the amount of data that has to be stored to create a polygon. Arcs or lines would create the polygon. Nodes are the end points of the arcs and the other points along the line are called shape points. Shape points are less important points compared to nodes. The computer reconstructs the polygon by going back to these nodes and creating the arcs of lines.

Raster

The raster data model is composed of a grid and each cell within the grid holds data. Another way to explain it is that the polygon has a grid laid over it and the polygon would fill those cells with data, each cell in the grid being assigned a value.

In the raster format the attribute is directly in the raster grid. The codes will equal features. This might mean multiple attributes to show the depth of a lake. There are five main elements to raster data. The first is that the cell size determines the resolution of the data and the cell has both ground and map expression. Second, the grid has an extent, that is rectangular since the grid is made of rows and columns. Also each cell has to be coded with something even if it is outside the area being worked on. The third element is the imperfect fit that is created by the grid; this means that there can be uneven widths of lines. Fourth, each cell can only hold one type of data despite the attribute ending half way through the cell. Last, every cell has to be big enough to hold the largest value of the attribute to be stored in the grid (p.74).

Raster is easier to work with and do overlays. It is also capable of rapid retrieval and analysis. It is easier to draw on the screen and on computer devices that display pixels. It also works better with constant variation in the data like elevation. There are two major drawbacks to raster. First, each pixel covers a certain area so numerous pixels are needed which means large files. Second, the maps also have a stair-step appearance because of the grid style.

Other Forms of Coding

Two other methods of graphic input are polar coordinates and Freeman Chain code. Within a polar coordinate system points are defined using the angle from the origin and the distance from the center. The Freeman Chain code uses a series of numbers to indicate movements from a current position. A star shape is used; this star has eight points that are numbered from 0 to 7. This means that there are eight possible movements. With each movement a new star is created at that point. Because the diagonal points are longer then the horizontal and vertical some compensation has to be made with this method.

For more information try this University of Washington site. Submitted by Amy Schaeufele, Febraury 4, 1998