Interpolation Algorithm-depicts God's face

Things are continuous, and time is continuous... the real world is mostly continuous.

However, we can only observe discretization for two reasons:

1. If the storage space required for consecutive records is too large, it is like the records cannot be accurate to ××× seconds.

2. We get that the data is discrete. A-> B-> C knows that records of A and C can be estimated by interpolation.

When we only have discrete point data and want to know the value of no data point, we can use interpolation, interpolation to fit the curve, or fitting

Plane, or even surface...

However, there are many interpolation models. We do not know what the original model is because we do not know what the original model is. This leads to a conflict.

What interpolation equations should we use for interpolation of known data? There is also the effectiveness evaluation of interpolation... All of this may be based on probability...

Perhaps what we can do is to select an appropriate interpolation model to fit the existing data... but what kind of model is appropriate requires experience... statistic method to judge .... no one knows what kind of model the real data is in. The surface or curve of a finite point is infinite... what we do is to simply approach the complexity ....

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Some interpolation algorithms (from the Internet)

Inverse Distance to a power (Inverse Distance Weighted Interpolation)
Kerkin Interpolation Method)
Minimum curvature (minimum curvature)
Modified Xie ARD's method (improved Xie bind's method)
Natural Neighbor (natural neighbor interpolation method)
Nearest Neighbor (nearest neighbor interpolation method)
Polynomial Regression (multivariate regression)
Radial Basis Function (Radial Basis Function)
Triangulation with linear interpolation (linear interpolation triangle method)
Moving Average (moving average method)
Local polynomial (local polynomial method)
The following describes the features of different algorithms.

1. distance reciprocal multiplication method
The distance reciprocal square gridded method is a weighted average interpolation method that can be used for exact or smooth interpolation. The square parameter controls how the weight coefficient decreases as the distance from a grid node increases. For a large cube, a relatively high weight share is given for a closer data point. For a smaller cube, the weights are evenly distributed to data points. When a grid node is computed, the weight of a specific data point is proportional to the reciprocal of the distance from the specified node to the observation point. When a grid endpoint is calculated, the assigned weight is a score, and the total weight is 1.0. When an observation point and a grid node are duplicated, the observation point is given a weight of 1.0 actually, and all other observation points are given a weight of almost 0.0. In other words, the node is assigned a value consistent with the observation point. This is an accurate interpolation. One of the features of the distance reciprocal method is to generate a "bull eye" around the observation point position in the grid area ". You can specify a smooth parameter when using the reciprocal distance grid. Smooth parameter guarantee with a value greater than zero. For a specific node, no observation point is assigned all the weights, even if the observation point overlaps with the node. Smooth parameters reduce the effect of the "Ox eye" by smoothing the grid that has been interpolated.

2. Kerry kingfa
The kerkin method is a grid method of geological statistics that is useful in many fields. Kerry kingfa tries to show the trend that is hidden in your data. For example, a high point is connected along a ridge, rather than isolated by a ox-Eye contour. The Kerry kingfa includes several factors: the change graph model, the drift type and the block effect.

3. Least Curvature Method
The least curvature method is widely used in Earth science. The interpolation surface generated by the least curvature method is similar to a long thin elastic slice with the minimum bending volume through each data value. The least curvature method tries to generate as smooth a surface as possible while respecting data as strictly as possible. When using the least curvature method, two parameters are involved: the maximum residual parameter and the maximum number of cycles parameter to control the convergence standard of the minimum curvature.

4. Multiple Regression
Multiple regression is used to determine the large-scale trend and pattern of your data. You can use several options to determine the type of the trend surface you need. In fact, multivariate regression is not an interpolation tool because it does not attempt to predict unknown Z values. It is actually a trend surface analysis and plotting program. When using multivariate regression, you must define the surface and specify the highest level of xy. The surface definition is the Polynomial Type of the selected data, these types are simple plane, bilinear saddle, quadratic surface, cubic surface, and user-defined polynomials. The parameter setting is the highest level of the X and Y elements in the polynomial equation.

5. Radial Basic Function Method
The radial basic function method is a combination of multiple data interpolation methods. According to the ability to adapt to your data and generate a smooth surface, the complex quadratic function is considered by many people as the best method. All basic radial function methods are accurate interpolation tools, and they all need to work to respect your data. To try to generate a smoother surface, you can introduce a smoother coefficient to all of these methods. The function you can specify is similar to the Change chart in Kerry. When interpolation is performed on a grid node, these functions specify a set of Optimal Weights for data points.

6. Xie binfa
Xie bind's method uses the least squares weighted by reciprocal distance. Therefore, it is similar to the reciprocal square interpolation, but it uses the local Least Square to remove or reduce the appearance of the generated contour. Xie beide can be an accurate or smooth interpolation tool. When using the Xie bind method as the grid method, the smooth parameter settings must be involved. Smooth parameters enable Xie bind to work like a smooth interpolation device. When you increase the value of a smooth parameter, the better the smooth effect is.

7. Tin/linear interpolation
The Triangle network interpolation tool is a strict interpolation tool, and its working route is similar to that drawn by hand. This method works by establishing several triangles by connecting data points. The connection method of the original data points is as follows: the edges of all triangles cannot interwork with other triangles. The result is a mesh that covers the grid and is spliced by triangles. Each triangle defines an area that covers the grid nodes in the triangle. The Skew and elevation of a triangle are determined by the three original data points that define the triangle. All nodes in a given triangle are restricted by the surface of the triangle. Because the original data points are used to define various triangles, your data is very respected.

8. natural neighbor interpolation
The natural neighboring point interpolation method (naturalneighbor) is a new method of mesh developed by surfer7.0. The natural neighbor interpolation method is widely used in some research fields. The basic principle is that for a group of Tyson (Thiessen) polygon, when a new data point (target) is added to the data set, these Tucson polygon will be modified, the weighted average value of neighboring points determines the weight of the point to be inserted. The weight of the point to be inserted is proportional to the weight of the target Taizhou polygon [9]. In fact, in these polygon, some polygon will be reduced, and no polygon will increase in size. At the same time, the natural neighbor interpolation method does not push out the contour lines (such as the contour lines of the taisen polygon) when the data point is raised ).

9. Nearest Neighbor Interpolation
Nearestneighbor (nearestneighbor) is also known as the Tucson Polygon method. The thiesen (also called Dirichlet or KNN polygon) method is an analytical method proposed by Dutch Meteorological scientist A. H. Thiessen. It was originally used to calculate the average rainfall from the rainfall data of the discrete distribution weather station. in GIS and geographic analysis, the tysen polygon is often used for quick assignment [2]. In fact, an implicit assumption of nearest neighbor interpolation is that the attribute values of P (x, y) of any mesh point use the attribute values of the point closest to it, use the neighborhood value of each grid node as the node value to be [3]. When data is already evenly distributed at intervals, You need to first convert the data to a surfer GRID file, you can apply the nearest neighbor interpolation method; or in a file, the data is closely complete, only a few vertices have no value. You can use the nearest neighbor interpolation method to fill in data points without value. Sometimes it is necessary to exclude the areas with no value data in the grid file, set a value in the search elliptic (searchellipse), and assign the blank value to the area without data in the grid file. The size of the search radius is smaller than the distance between the data values of the grid file. All nodes without a data grid are assigned a blank value. When using the nearest neighbor interpolation gridded method to convert XYZ data at a regular interval to a grid file, you can set equal spacing between the grid interval and the data points of XYZ data. The nearest neighbor interpolation gridded method has no options. It is homogeneous and non-changing, and is useful for interpolation of data with even intervals. At the same time, it is very effective for filling areas with no value data.