#!F-adobe-helvetica-medium-r-normal--18* #!N #!CSeaGreen #!N #!Rall190 Positions and Connections Dependence #!N #!EC #!N #!N The concept of sampling should be familiar to anyone who has ever collected data on some kind of grid. For example, a botanist may lay down a series of square grid markers over an area of interest then count the numbers of species of grasses growing inside each grid square. The number so collected becomes a sample value or datum associated with that grid marker. A single number like this, whether floating point or integer, is called a #!F-adobe-times-medium-i-normal--18* scalar #!EF . If the wind velocity and direction at, say, the center of each grid square is also measured, the botanist would record a #!F-adobe-times-medium-i-normal--18* vector #!EF quantity as a second datum sampled at the same place. A vector encodes both direction and magnitude with two or more numeric "vector components." #!N #!N In this example, the locations of the corners of each grid marker are recorded as an array of 2-dimensional coordinates that define the sampling area dimensions and the sampling resolution. In computer graphics terms, these spatial location points are called #!F-adobe-times-medium-i-normal--18* vertices #!EF (singular: vertex); in Data Explorer, they are referred to as "positions." Loosely, everyone calls them "points." #!N #!N Four coordinate positions can be connected by a quadrilateral to define a grid #!F-adobe-times-medium-i-normal--18* element #!EF . The quadrilateral itself is called a #!F-adobe-times-medium-i-normal--18* connection #!EF in Data Explorer (we will discuss other connection types in a moment). Since the botanist collected one set of data per grid element, such data are termed #!F-adobe-times-medium-i-normal--18* connection-dependent data #!EF . This implies that the data value is assumed by Data Explorer to be constant within that element. #!N #!N Consider another technique for data sampling: on a larger scale, remote-sensing satellites can resolve various features of the Earth down to some finite level of resolution. In this case, the grid positions are identified by a latitude-longitude coordinate pair, and the data values may encode such things as surface reflectance in the ultraviolet. By associating each data value with a latitude-longitude position, we produce #!F-adobe-times-medium-i-normal--18* position-dependent data #!EF . #!N #!N This implies that data values should be interpolated between positions, using the connections (grid) if one is present. Data Explorer works equally well with position-dependent and connection-dependent data (see #!Lcpdpnd20,dxall191 f Figure 20 #!EL ). #!Cbrown #!N #!F-adobe-times-medium-r-normal--18* #!Rcpdpnd20 #!N Graphics omitted from Online Documentation. Please see the manual. #!N #!N Figure 20. Examples of Data Dependency #!EF #!N #!EC Generally, the decision about which dependency the data has is made by you at the time of data collection or simulation. (There is a simple way in Data Explorer to convert either dependency to the other. See #!Lpost,dxall910 h Post #!EL in IBM Visualization Data Explorer User's Reference.) #!N #!N We can extend our data sampling into three dimensions where appropriate. In that case, we identify each grid position with three coordinates. These coordinates form the corners of "volumetric" elements and the entire sample space is called a #!F-adobe-times-medium-i-normal--18* volume #!EF . A volumetric element may be a rectangular prism (like a #!F-adobe-times-medium-i-normal--18* cube #!EF ) or a #!F-adobe-times-medium-i-normal--18* tetrahedron #!EF (a solid with four triangular faces, not necessarily equilateral). #!N #!N #!N #!F-adobe-times-medium-i-normal--18* Next Topic #!EF #!N #!N #!Lall191,dxall192 h Connections and Interpolation #!EL #!N #!F-adobe-times-medium-i-normal--18* #!N
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