Lecture 18Iterative Operations
Learning Objectives
18.1 Describe the basic principle underlying an iterative intervisibility operation for viewshed.
18.2 Describe the basic principle underlying a cost accumulation operation.
18.3 Describe the basic principle underlying a drainage flow accumulation operation.
18.4 Describe the basic principle of network cost accumulation using node-star data structure.
Iterative operations (those that repeat over and over) allow us to process data across space and/or time. Iterative operations use a series of neighborhood operations to move a local result into a broaderspace, time, attribute or a combination context.
Example iterative operations:
- Viewshed–line of sight “rays” project to visual obstructionsdeterminingvisibility
- Cost Accumulation- propagate cost to neighbors (commonly) across a surface
- Water Drainage- accumulate flow downhill to a pour point
- Transportation Network – find shortest path along routes
Viewshed using intervisibility
18.1 Describe the basic principle underlying a iterative intervisibility operation for viewshed.
Intervisibility (line of sight) can be computed using a set of rays radiating outwards from a vantage point. On a surface, locations (cells) on the surface obstruct a view by rising above the line of sight. Intervisibility can be applied to human visionlike scenic beauty such as viewing mountains or lakes, or other viewing forms of electromagnetic radiation, such as FM radios, cellular telephones and personal communication networks. esriwhitepaper about 3D analystdescribes the intervisibility operations.
From a given vantage point (or multiple points), aviewshedis the areathat can beseen. Viewshed assembles all the locationsinto areaswhere the “line of sight is clear” as the rays move outwards from the point. A cross-section diagram through a surface is shown below as “line of sight” ray tracing.
A procedure to calculate viewshed operates through iteration working outwards. A 'horizon line' holds the highest vertical angle yet seen in each direction. A new location (such as a cell in a raster implementation) is tested against the horizon line to check if it is hidden (below) or visible (above). Locations must be visited in the order in which they might be seen. Visible locations (yes/no visible values) from a single cell are marked as a part of the viewshed for that cell.
Yes/no visible values from each particular place (cell) in question can be summed for a collection of locations (or all locations for that matter) to create a cumulative viewshed map. For example, in the Madaba Plains of Jordan, social interaction among settlements is being studied, and a cumulative viewshed map (see Fig 8) for multiple watch towers has been computed.
What influences the viewshed intervisibility?
Viewshed calculations depend upon an accurate landscape model of the surface as seen. Thus, elevation is a key component. Topographic maps and topographic databases are constructed for highway engineers, artillery officers, and resort managersto portray view surface as appropriate to their need. Land cover can matter. Vegetation screens the line of sight for many wavelengths (but not all). Vegetation effects are rarely measured, but often added to a surface by adding a constant for each land cover class. Viewer height can also influence the viewshed result as given in figure below.
Other example applications of viewsheds:
- Vista Scenic Beauty
- Cell-phone towers
- Collection of articles about viewshed GIS
A review of articles provides further insight about line of sight analysis – see chapter 6.
Cost Accumulation
18.2 Describe the basic principle underlying a cost accumulation operation.
An iterative operation can work with a contributory rule to accumulate the total 'cost' outwards from a 'source'. This modifies a bufferanalysis byusing a measure of “cost”(cost interpreted with units such as time or effort, impedance (drag), distance, and/or difficulty, all viewed as ‘friction’ across a surface. Cost units must be converted toa common measurement unit so we can ‘sum’ them.
First, a realistic cost must be assigned to traverse each area. This approach is easier for cells, but it could be done for any set of vector zones. Then, it may be necessary to convert the cost to traverse a cell into a rate to handle diagonal movement properly. An isolated object (e.g., point, or line or boundary line) provides the starting location. In graphic below a SPREAD operationmoves the cost outwards in an iterative manner. The operation is not strictly geometrical. It is possible for a second 'attribute value' to provide an additional cost (e.g., passing around a hill in the cost surface as a lump barrier) to be included when arriving at cost. The result is a cost accumulation surfacederived through an iterative computation.
Examples of cost accumulation.Building and analyzing cost surfaces.Examples;cost accumulation in GRASS;cost surface for autonomous vehicle routing;
Water Drainage
18.3 Describe the basic principle underlying a drainage flow accumulation operation.
Drainage makes use of a topographic surface as described previous lectures.
Water will flow from higher locations (cells, triangles, etc.) downwards.
Accumulation of water is computed byiterating through slope (neighbor azimuth and neighbor gradient).
Lab assignment about Flow Operations on Surfaces is an example of iterative operations based on Lecture 14.
An overview of flow direction in multiple domains can be found here.
Transportation Network
18.4 Describe the basic principle of network cost accumulation using node-star data structure.
Finding shortest path distance in a network uses iterative operations ona node-star data structure. Nodes are connected by links (segments / chains). A node-star is a node with all the links that connect into/out from that node.
For a specified origin and destination, compute the accumulated distance to next node in network.
Check to see if that node is in the node list from the other node.
Local accumulations can actually be pre-computed and stored for each node in network.
They are then sampled when origins and destinations are chosen, and “traced” to check node matching.
The goal is to have the fewest units accumulated from origin to destination.
The esriArcGIS Network Analyst extension implements iterative operations for transportation networks using a node-star data structure.