Time for some more "high concept" work. This time we'll tackle the idea of "dependency" which describes how Fields relate the various Components to each other.
In data collection, researchers apply different strategies for different types of data. The two most common sampling strategies are these:
- Data is considered to be sampled at points in space
- Data is considered to be sampled over areas in space
For example, many scientific instruments have a sensor that samples a limited spatial domain near its input and the data is considered to be a "point" sample. Many samples are gathered and in a lot of cases, it is scientifically sound to interpolate over the sampled spatial domain to calculate values in between these point samples.
Other devices are considered to sample over an area whose extent is large relative to the entire sampled domain. For example, some remote sensing satellite devices measure areas on the Earth surface on the order of 30m square (one pixel on a remote sensed image). Because this areal size is larger than some ground features, it is not appropriate to interpolate to get in-between values (what's the average between forest and pond?), so the data is considered to be constant over the entire area of each sample.
Computational simulations may be one or the other depending on the type of phenomenon being simulated.
Here's an illustration to make this clear:
DX uses this terminology for the two sampling schemes: point sampled data is called "position dependent" because the data is sampled at the locations which we list in the "positions" Component. Areal sampled data is called "connection dependent" because each datum is associated with the interpolation line, surface, or volume element as a whole. To see how the same data would look if it were measured at vertices (grid intersections, in this case), or over the whole of each grid cell, look at this illustration:
The dependency equation has another feature: if you describe your data as being "position dependent", DX expects your data object to contain exactly as many data values as there are positions. If you describe it as "connection dependent", you must have the same number of connection elements as data values.
