tailieunhanh - KEY CONCEPTS & TECHNIQUES IN GIS Part 7

Việc thực hiện của IDW khác nhau giữa các gói phần mềm, nhưng hầu hết trong số họ cho phép đặc điểm kỹ thuật của các số và hoặc khoảng cách của giá trị đã biết để được bao gồm, và theo thứ tự để hoạt động đúng cách họ phải cho phép cho người sử dụng chỉ định các tỷ lệ mà tại đó một của vị trí trọng lượng giảmtheo khoảng cách. | 66 KEY CONCEPTS AND TECHNIQUES IN GIS Figure 52 Inverse distance weighting the calculation is repeated for every cell for which we don t have a measurement. The implementation of IDW differs among software packages but most of them allow specification of the number and or distance of known values to be included and in order to function properly they must allow for the user to specify the rate at which a location s weight decreases over distance. The differences lie in how sophisticated that distance-decay function can be. Because IDW calculates new values only for points for which no measurements exist it does not touch the values of known locations and hence is an exact interpolator. Global and local polynomials Most readers will remember polynomials from their high school geometry classes. These are equations that we use to fit a line or curve through a number of known points. We encountered them in their simplest form in the calculation of slope usually described in the formy a bx. Here we fit a straight line between two points which works perfectly well in a raster GIS where the distance from one elevation value to the next is minimal. If the distance between the measured point locations is large however then a straight line is unlikely to adequately represent the surface it would also be highly unusual for all the measured points to line up along a straight line see Figure 53 . Polynomials of second or higher degree the number of plus or minus signs in the equation determines the degree of a polynomial represent the actual surface much better. Increasingly higher degrees have two disadvantages. First the math to solve higher degree polynomials is quite complicated remember your geometry class . Second even more importantly a very sophisticated equation is likely to be an overfit. An overfit occurs when the equation is made to fit one particular set of input points but gets thrown off when that set changes or even when just one other point is added. In .