Section Four - Discrete and Continuous Data

The spatial distribution of raster and vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects can be placed into two descriptive categories: discrete data Discrete data, which is sometimes called thematic, categorical, or discontinuous data, most often represents objects in both the feature (vector) and raster data Raster data is a type of digital data that stores information about a location using a grid of pixels or cells. All spatial rasters are raster files, but not all raster files are spatial rasters. storage systems. A discrete object has known and definable boundaries: it is easy to define precisely where the object begins and where it ends. and continuous data A continuous surface represents phenomena in which each location on the surface is a measure of the concentration level or its relationship from a fixed point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. in space or from an emitting source. . While both raster and vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects can contain data with either discrete or continuous, most often, vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects is described as discrete while raster is described as continuous.

3.4.1: Discrete Data

Discrete data is data that represents features which can exist independently with clear and definable boundaries, even when part of a larger data set. For example, a vector layer (a generic name for spatial data Data that deals with location, such as lists of addresses, the footprint of a building, the boundaries of cities and counties, etc. ) showing the continental United States could be categorized as discrete data Discrete data, which is sometimes called thematic, categorical, or discontinuous data, most often represents objects in both the feature (vector) and raster data Raster data is a type of digital data that stores information about a location using a grid of pixels or cells. All spatial rasters are raster files, but not all raster files are spatial rasters. storage systems. A discrete object has known and definable boundaries: it is easy to define precisely where the object begins and where it ends. . The United States has a clear and definable administrative boundary, as does each state in the Union. The State of Colorado could continue to exist even if all the other states suddenly dissolved their boundaries; similarly, we can have a map of just Colorado. Discrete data can be any of the three geometries: points, polylines, or polygons, or one or many pixels of a raster layer.

3.4.2: Continuous Data

Continuous data is the opposite of discrete data Discrete data, which is sometimes called thematic, categorical, or discontinuous data, most often represents objects in both the feature (vector) and raster data Raster data is a type of digital data that stores information about a location using a grid of pixels or cells. All spatial rasters are raster files, but not all raster files are spatial rasters. storage systems. A discrete object has known and definable boundaries: it is easy to define precisely where the object begins and where it ends. , data which does not have clear and definable boundaries, but instead makes a "blanket" of data across a landscape, defined with interval-ratio of values. Continuous data will continue to exist even if you take away one portion of it (which is impossible). Even if you removed 75°F from the English language, 75°F will not cease to exist. Just because it doesn't have a label doesn't mean it doesn't exist or you have no comprehension of what it is. If Colorado, represented by discrete data Discrete data, which is sometimes called thematic, categorical, or discontinuous data, most often represents objects in both the feature (vector) and raster data Raster data is a type of digital data that stores information about a location using a grid of pixels or cells. All spatial rasters are raster files, but not all raster files are spatial rasters. storage systems. A discrete object has known and definable boundaries: it is easy to define precisely where the object begins and where it ends. , was absorbed by Kansas and a new border was drawn, future generations would not have experience with Colorado or Kansas - their reality might be Kansarado, a state with a clear and define boundary. They wouldn't have a comprehension of Colorado or Kansas as independent objects.

Data such as temperature, precipitation, elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface , slope A numeric value - either in percent or degree - expressing the steepness or the rise/run of the landscape. , and aspect [geographic coordinate systems] The direction the developable surface a geometric shape which will not be distorted when flattened. Used as the base shape to transfer features during projections. Most often a cone, cylinder, or plane (azimuthal) faces in relation to the geographic coordinate system. Normal; transverse, oblique[topography] The cardinal direction a slope A numeric value - either in percent or degree - expressing the steepness or the rise/run of the landscape. faces (NSEW) are all examples of continuous data A continuous surface represents phenomena in which each location on the surface is a measure of the concentration level or its relationship from a fixed point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. in space or from an emitting source. . Each defined value on the scale of descriptive values must exist in order to arrive at the next one. Slopes (with the exception of cliffs) do not just change from 0% to 47% by taking one step forward on a hike. The slope A numeric value - either in percent or degree - expressing the steepness or the rise/run of the landscape. must pass through all of the percentages to gradually rise (some places that rise is much more rapid, but the slope A numeric value - either in percent or degree - expressing the steepness or the rise/run of the landscape. must still pass through all the values first).

Most often, classified raster data Raster data is a type of digital data that stores information about a location using a grid of pixels or cells. All spatial rasters are raster files, but not all raster files are spatial rasters. is continuous data A continuous surface represents phenomena in which each location on the surface is a measure of the concentration level or its relationship from a fixed point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. in space or from an emitting source. , and from those continuous layers, we can extract the information we would need to create discrete data Discrete data, which is sometimes called thematic, categorical, or discontinuous data, most often represents objects in both the feature (vector) and raster data Raster data is a type of digital data that stores information about a location using a grid of pixels or cells. All spatial rasters are raster files, but not all raster files are spatial rasters. storage systems. A discrete object has known and definable boundaries: it is easy to define precisely where the object begins and where it ends. . For example, I might start with a DEM Digital Elevation Model , which is a continuous expression of elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface , from which I can extract slope A numeric value - either in percent or degree - expressing the steepness or the rise/run of the landscape. or aspect [geographic coordinate systems] The direction the developable surface a geometric shape which will not be distorted when flattened. Used as the base shape to transfer features during projections. Most often a cone, cylinder, or plane (azimuthal) faces in relation to the geographic coordinate system. Normal; transverse, oblique[topography] The cardinal direction a slope A numeric value - either in percent or degree - expressing the steepness or the rise/run of the landscape. faces (NSEW) . From those layers, I can subset just the slopes between 10 and 40°, and define that discretely as the preferred area for a particular nesting bird.

Students sometimes have problems with the fact that continuous data A continuous surface represents phenomena in which each location on the surface is a measure of the concentration level or its relationship from a fixed point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. in space or from an emitting source. appears to be discrete in the software. For example, in the "Geothermal Resource of the United States" map found in Figure 3.13, the swirled red, orange, yellow, and greens across the map show a continuous range of data classified between "Most Favorable" and "Least Favorable". Within these swirls, it appears that where the red stops, the orange begins. While this is true when looking at the map, it's not exactly how it is in real life. Since we know the definition of a map to be: a scale, symbolized, generalized model of reality, we need to both symbolize and generalize the data. In order for the data to coexist on the map and conform to the limitations of the software, computer monitor, and printer, each color needs to stop somewhere for the next to begin. If you keep continuous data A continuous surface represents phenomena in which each location on the surface is a measure of the concentration level or its relationship from a fixed point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. in space or from an emitting source. in your mind as "data without defined boundaries covering a scale of values" and discrete data Discrete data, which is sometimes called thematic, categorical, or discontinuous data, most often represents objects in both the feature (vector) and raster data Raster data is a type of digital data that stores information about a location using a grid of pixels or cells. All spatial rasters are raster files, but not all raster files are spatial rasters. storage systems. A discrete object has known and definable boundaries: it is easy to define precisely where the object begins and where it ends. as "data with clear, defined, movable boundaries described with values which can be removed from a system without destroying the entire system", you will understand the difference.

Figure 3.14: An Example of Discrete and Continuous Data Displayed on a Single Map

Within the GIS Geographic Information Systems the software used to create, store, and manage spatial data Data that deals with location, such as lists of addresses, the footprint of a building, the boundaries of cities and counties, etc. , analyze spatial problems, and display the data in cartographic layouts Geographic Information Sciences , it's important to understand the difference between continuous and discrete data Discrete data, which is sometimes called thematic, categorical, or discontinuous data, most often represents objects in both the feature (vector) and raster data Raster data is a type of digital data that stores information about a location using a grid of pixels or cells. All spatial rasters are raster files, but not all raster files are spatial rasters. storage systems. A discrete object has known and definable boundaries: it is easy to define precisely where the object begins and where it ends. , as they are often referred to by name in geoprocessing and cartographic tools. Due to the properties of discrete and continuous data A continuous surface represents phenomena in which each location on the surface is a measure of the concentration level or its relationship from a fixed point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. in space or from an emitting source. , the software processes and displays them differently, using totally different base calculus (which you don't need to know, just know it exists in the background).

3.4.3: Examples of Discrete and Continuous Data

Discrete data is fairly easy to image and understand - almost all used in the is . Below, we look at some examples of vector datasets that are continuous and sets which are discrete (since we looked at continuous examples in Section Three: Raster Data).

Figure 3.15: Examples of Discrete Data

Three examples of - , , and polygon.

Triangulated Irregular Networks (TINs) and Contour Lines

Triangulated Irregular Networks (TINs) are a special kind of vector file which show continuous elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface over a landscape. Notice the TIN is a series of triangles, representing the landscape as a blanket while the contour lines show the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface in a decreasing manner. Notice the TIN is a series of triangles, representing the landscape as a blanket while the contour lines show the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface in a decreasing manner. TINs are used to create contour lines (described below), which is why you see contour lines on topographic maps and not TINs.

TINs are created from an input layer of either: a series of elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface points measured across the landscape or a DEM Digital Elevation Model . When the input is a series of points, the tool connects each point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. to two other points around it, creating an irregular pattern (network) of triangles where each triangle represents a portion of the slope A numeric value - either in percent or degree - expressing the steepness or the rise/run of the landscape. on a hill side. When the input is a DEM Digital Elevation Model , each value associated with one pixel The smallest unit of information in a digital image or raster map, usually square or rectangular. Often used synonymously with cell. Pixel is an abbreviation of "picture element". is connected to two other similar or same values in neighboring pixels, resulting in the same irregular network of triangles. TINs are not used in GIS Geographic Information Systems the software used to create, store, and manage spatial data Data that deals with location, such as lists of addresses, the footprint of a building, the boundaries of cities and counties, etc. , analyze spatial problems, and display the data in cartographic layouts Geographic Information Sciences 101, however, it's important to know they exist.

Figure 3.16: A TIN with Contour Lines Drawn Over

The TIN (shown with blue lines) can be seen below the contour lines (shown in red and white)

Contour Lines

Contour lines are another example of continuous vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects . Created from a TIN, a DEM Digital Elevation Model , or a series of surveyed points stored in a vector point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. file, contour lines connect together all the points of equal elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface . While you can set the contour interval, or the equal gain or loss in elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface from one contour line to the next, the most common methods are by intervals of ten. The software creates the contour lines using a geoprocessing tool, with a user input of the elevation the vertical distance between local mean sea level the measurement above or below the global average at a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features and a single point A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of just one vertex pl. vertices One of a set of ordered x,y coordinate pairs that defines the shape of a line or polygon feature. , marking a single XY location in any given geographic or projected coordinate system. on the Earth's surface -based file (TIN or DEM Digital Elevation Model , usually) and a contour interval (often 10, 50, 100). The output file is a polyline A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of two or more vertices connected by straight lines. Often used to represent objects such as roads, river, and boundaries. file, which uses the polyline A GIS vector data in any sort of digital science or art, is simply denoting a type of graphical representation using straight lines to construct the outlines of objects geometry type which is made up of two or more vertices connected by straight lines. Often used to represent objects such as roads, river, and boundaries. file icon , with a user-defined name.

Figure 3.17: A Very Close Up of Contour Lines Over an Elevation Point Layer

Contour lines, whether created from a TIN, a , or a layer, are all formed in the same way: or pixels of equal are determined by the software and then connected with lines. Each contour line represents one , with the next having a