Tech Tip: Units and Accuracy

Accuracy in Conversions

Network Import Shapes Vary by Units Used

Accuracy in Conversions

Manifold uses integer coordinates to achieve speed and robustness in critical geometric operations. This means we do truncation when getting data from a floating-point source (import, editing inside ObjectCoordinates dialog, etc.) However, it is possible to keep the desired accuracy within Manifold up to very high limits. The limit is reached when the overall coordinate data domain expressed in data resolution units (e.g. size of Nevada expressed in centimeters) exceeds 10^9.

UTM is a good example of this. First, decide what accuracy is required for data. UTM uses meters by default so let's suppose we want centimeters instead. When the accuracy is chosen, compute the coordinate translation factor needed to go from the existing units to the desired units. For example, if we are going from meters to centimeters each coordinate should be multiplied by 100. A coordinate of 2.11 will become 211. It is best to try to make the translation factor an integer.

After that, go into Access and multiply every coordinate by the translation factor. [If you are not one of those lucky people who has the Manifold Calculator for Access, you will need to use update queries to accomplish this.] After the translation factor has been applied to the X and Y or Lat and Lon coordinates, import the map into Manifold, then go to Options and set the meter-to-units value to the right of the "1 meter =" prompt to the translation factor (100 in our example). Now you have the same map with better accuracy.

Tip: Never, never exceed the 10^9 boundary as the coordinates would then wrap towards zero. Here is how to be sure it doesn't get exceeded when improving the conversion accuracy level of an existing map:

• Run the Geometry/Measurement/ExtremalCoords solver on "all layers" to find the largest and smallest coordinates in the existing map rectangle.

• Multiply each extremal coordinate by the translation factor you propose to apply to the map. (100 in our example of using centimeters instead of meters) to see if applying the translation factor puts any of the extremal values outside the range -10^9..10^9.
  

Network Import Shapes Vary by Units Used

This problem involves coordinate units. The Manifold network import solver imports a network into a circle with a given center and radius. To choose a radius you select the desired measurement unit from a combo box and enter a value (e.g. 5 miles). By default, the solver uses a value of 1 and current measurement units.

Because Manifold uses integer coordinates for objects (see above), there is a "natural" unit of measurement relationship that consists of what should be the physical distance between two points at any given abstract coordinates (for example, beween 0,0 and 1,0 or between 100,100 and 100,101).

This unit of measurement relationship may consist of different physical values for different maps, so Manifold allows each map to have a "meters per unit" (or "degrees per unit" for geographical maps in lon/lat) parameter that can be specified within the Options dialog. By default 1 unit equals 1 meter (for lan/lon geographic maps, 10000 units equal 1 degree).

When we import a network into a 1-mile circle, Manifold places points representing nodes within a  circle that has a radius of 1609 units since by default one unit is one meter and there are 1609 meters per mile. However, when we import a network into a 1-meter circle, Manifold places points onto a circle of only one unit in radius. Since we use integer coordinates we have only 9 possible coordinate values at which we can place the points:

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