Introduction to common interpolation methods

Introduction to common interpolation methods

Inverse Distance to a Power (inverse distance weighted interpolation), "Kriging (kriging)", "Minimum curvature (minimum curvature)", "Modified Shepard" s method (improved Xie de) "," Natural Neighbor (Natural neighbor interpolation method) "," Nearest Neighbor (Nearest neighbor interpolation method) "," Polynomial Regression (multivariate regression method) "," Radial Basis function (Radial basis function method) "," Triangulation with Linear interpolation (linear interpolation triangulation) "," moving Average (moving average method) "," Local Polynomial (local polynomial method) " 1, the distance reciprocal multiplication method distance reciprocal multiplication grid method is a weighted average interpolation method, you can do the exact or the smooth way interpolation. Square parameter Controls how the weight factor decreases as the distance from a grid node increases. For a larger square, the closer data points are Given a higher weight share, for a smaller party, the weights are evenly distributed to each data point. When a grid node is computed, the weights given to a particular data point are assigned to the node of the specified square from the node to the point of observation. Proportional to the countdown. When calculating a grid node, the assigned weight is a fraction, and the sum of the weights equals 1.0. When a When the observation point coincides with a grid node, the observation point is given an actual weight of 1.0, and all other observation points are given a A weight of almost 0.0. In other words, the node is assigned a value that is consistent with the observation point. This is an accurate interpolation. One of the characteristics of the distance reciprocal method is to produce a "bull eye" around the location of the observation point within the grid area. The grid of the countdown grid can be To specify a smoothing parameter. A smooth parameter greater than 0 guarantees that no observation point is given to a particular node. Even if the observation point is coincident with the node. The smoothing parameters reduce the "bull eye" effect by trimming the grid that has been interpolated. 2, Krigin Fakkerikin method is a kind of geological statistic grid method which is very useful in many fields. Kriging trying to express that implied in your number According to the trend, for example, the highs would be connected along a ridge, rather than being isolated by the bull-eye contour. Kriging includes several factors: the change graph model, the drift type, and the nugget effect. 3, the minimum curvature method is widely used in Earth science. The interpolation surface generated by the minimum curvature method is similar to a single data value, with the most A thin long strip of elastic sheet with small bending amount. Minimum curvature method, which attempts to produce as smooth a as possible while respecting data as closely as possible Surface. Two parameters are involved when using the minimum curvature method: maximum residual parameter and maximum number of cycles parameter to control the convergence of minimum curvature Standard. 4. Multivariate regression method multivariate regression is used to determine the large-scale trends and patterns of your data. You can use a few options to determine the trend surface class you need Type. Multivariate regression is not actually a interpolator because it does not attempt to predict unknown Z-values. It is actually a trend surface analysis made Diagram program. When using multivariate regression, it involves the surface definition and the highest quadratic setting of the specified XY, and the surface definition is a multi- Item types, which are simple planes, bilinear saddles, two-times surfaces, three-times surfaces, and user-defined polynomial, respectively. Parameter setting is the highest square of the X and Y elements in the specified polynomial equation. 5, Radial basic function Method radial basic function method is a combination of multiple data interpolation methods. Based on the ability to adapt your data and generate a sleek surface, where The complex two functions are considered by many to be the best method. All radial basic function methods are accurate interpolator, they all have to respect Your data and strive for it. To try to create a more rounded surface, you can introduce a smoothing factor for all of these methods. You A function that can be specified is similar to a change chart in a gram. When interpolating a grid node, these functions give the data point a Set the optimal weight. 6. The Shebed Fashebed method uses the least squares weighted by the distance. As a result, it is similar to the reciprocal exponentiation interpolator, but it A local least squares is used to eliminate or reduce the "bull eye" appearance of the generated contour lines. The Shebed method can be an accurate or rounded interpolation Manager When using SHEBEDFA as the grid method, the setting of the smoothing parameters is involved. The smoothing parameter is to make the Shebed method like a circle Work as a slide interpolator. When you increase the value of the rounded parameters, the smoother the better. 7, triangular network/linear interpolation triangle network interpolator is a strict interpolator, its work line and hand-drawn contour similar. This method is done by the number of A number of triangles are set up to work with the connections between the strongholds. This is how the original data points are linked: the edges of all triangles are not Can intersect with a different triangle. The result is a net covering the grid area, which is spliced together by triangles. Each triangle defines a polygon that covers the mesh nodes of the triangle. The triangle's tilt and elevation are defined by this triangle Three raw data points are determined. All nodes within a given triangle are constrained by the surface of the triangle. Because the original data point are used to define the various triangles, so your data is very respected. 8. The natural Neighbor interpolation method (Naturalneighbor) is a new meshing method of Surfer7.0. Natural neighboring points Interpolation method is widely used in some research fields. The rationale is for a group of Tyson (Thiessen) polygons, when added in the data set into a new data point (the target), these Tyson polygons are modified, and the weighted average of the neighbors determines the weights to be interpolated. , the weight of the insertion point and the target Tyson's multilateral form ratio [9]. In fact, in these polygons, some of the polygons will be smaller in size, And no polygon size will increase. At the same time, the natural neighbor interpolation method does not extrapolate the contour at the point where the data points are raised (such as Thai The contour line of the Sen Polygon). 9. Nearest neighbor interpolation method nearest neighbor interpolation (Nearestneighbor) is also called Tyson Polygon method, Tyson Polygon (Thiesen, also called D Irichlet or Voronoi polygon) analysis is an analytical method proposed by the Dutch meteorologist A.h.thiessen. Originally used to depart from The average rainfall is calculated in the rainfall data of the scattered meteorological stations, and the Tyson polygons are often used in GIS and geo-analysis to quickly Assigned value [2]. In fact, one implied assumption of the nearest neighbor interpolation is that the attribute value of either grid point P (x, y) is used from its nearest The attribute value of the location point, using the nearest point value of each grid node as the node value to be used [3]. When the data is already evenly spaced, To convert the data to a surfer grid file, you can apply the nearest neighbor interpolation method, or in a file, the data is tightly integrated and only There are few points that are not valued, and the nearest neighbor interpolation method is used to populate the data points without values. Sometimes you need to exclude data that is not valued in a grid file Area, set a value in the search ellipse (searchellipse), giving the blank value in the grid file to the infinite data region. Set the The search radius is smaller than the distance between the data values of the grid file, and all the non-data grid nodes are given a blank value. In making Grid interval and XYZ number can be set when converting XYZ data of a regular interval to a grid file using nearest neighbor interpolation meshing method The spacing between data points is equal. Nearest neighbor interpolation meshing method has no option, it is homogeneous and unchanged, the number of uniform intervals Interpolation is useful, and it works well for areas where no value data is populated.

Introduction to common interpolation methods