9. Depending on the input coordiantes and the query coordinates, it is not uncommon for the. 125) ans = 0. You can evaluate F at a set of query points, such as (xq,yq) in 2-D, to produce interpolated values vq = F (xq,yq). I post the resutls of the computational time: interp2:5. Issues. 5. xcoordinate,T. Use scatteredInterpolant to perform interpolation on a 2-D or 3-D data set of scattered data . this will generate X and Y of n by n. Exactly how you grid the data depends on the locations of the data points. Your program might issue warnings that do not always adversely affect execution. Copy. Description. These tools work via triangulations of the domain - Delaunay triangulations, which result in convex things. It is also significantly faster than this function and have support for extrapolation. This mesh is equivalent to the bounding box for Alaska. For your 3D case lets talk about computational geometry first, to understand why part of the region gives NaN from griddata. scatteredInterpolant returns the interpolant F for the given data set. The scatteredInterpolant class supports scattered data interpolation in 2-D and 3-D space. F = scatteredInterpolant(x,y,v) F = scatteredInterpolant(x,y,z,v)Generate a regular mesh from irregular data using interpolation. interpolate. Use griddedInterpolant to perform interpolation with gridded data. I have two data sets of different sizes, one of which is a 15x3 matrix of latitude, longitude, and concentration data and the other of which is a 2550x3 matrix, also composed of latitude, longitude, and concentration data. InterpolatePchipSorted instead, which is more efficient. Using scatteredinterpolant instead of. m uses the scatteredInterpolant function with default methods and may provide bumpy plots at the highest velocities, while the testPerfo1. " Does this mean that the function discovered duplicate (x,y) grid points in my inputs, or that some adjacent z-points are duplicated?Installation. The values v must be a column vector of. % Section Classification Flange width to thickness ratio in compression. Scattered data interpolation with multilevel B-Splines. You can use interpolation to fill-in missing data, smooth existing data, make predictions, and more. pos = [x y z] ef = [e_x e_y e_z] The matrices are 1000x3 in size, and the positions are located in a half sphere (cartesian coordinates). 0000 value in temperature column representing NaN or missing data. Sign in to answer this question. scatteredInterpolant 는 지정된 데이터 세트에 대해 보간 함수 F 를 반환합니다. 0 Comments. Hi, I am quite new to MatLab. Connect and share knowledge within a single location that is structured and easy to search. 0. scipy. The scatteredInterpolant function gives me "Warning: Duplicate data points have been detected and removed - corresponding values have been averaged. According to the docs scatteredInterpolant(x,y,v) takes x, y as points and v as surface data to interpolate. Thats why I need interpolation. Prototyping at the command line may not yield the same level of performance. x,y and v are vector (1x77), while xip and yip are sample points (1x51 and 1x21)Using the scatteredInterpolant class I was able to get velocity at any location I want. I would like to extrapolate a surface I have provided in Matlab. F = scatteredInterpolant (x_c,y_c,z_c);Walter Roberson on 9 Dec 2015. The goal is to create gridded data from scattered data. Historically, the MATLAB approach was to use qhull to produce a triangulation, and then for each query point, query which triangle it was in and use the vertices of the triangle to do the interpolation. S = scatteredInterpolant(x,y,z,d); Is there a way i could use something similar in Swift/Objective-c or any other compatible language to develop a small app for iOS (as well as for Android if possible) where i insert scattered data and when the user enter a value for a given X and Y he gets an interpolated value for Z (i intend to use this with. 000 417826. %coords supportPts = [3 3; 3. We do a lot of full field 3D numerical simulations (CFD, FEA, etc. You can evaluate F at a set of query points, such as (xq,yq) in 2-D, to produce interpolated values vq = F (xq,yq). scipy. % Class 2 taken to be the upper limit as same procedure as Class 1. y at z=0, I use griddata command to reshape my velocity vector into same n. V contains the corresponding function values at each sample point. 2-D array of data point coordinates, or a precomputed Delaunay triangulation. Gridded and scattered data interpolation, data gridding, piecewise polynomials. I tried to use the information in the following link ( with the scatteredInterpolant function ) however it is not. 6 3; 3. For computational purposes, I need to resample them over a grid with a used-defined space discretization (say, 5 m). Answered: Walter Roberson on 13 Aug 2020. I have a 256 x 256 x 32 grid of regularly spaced points ranging over x, y, and z and with an. import matplotlib. The MATLAB language is designed to give optimum performance when your application is structured into functions that reside in files. This function only allows to specify the query points but not the 'ConnectivityList' because internally it performs its own Delaunay triangulation from the specified point set. . 插值是在一组已知数据点的范围内添加新数据点的技术。. You can. The scatteredInterpolant class supports scattered data interpolation in 2-D and 3-D space. Teams. 1 Link griddedInterpolant -- if you do not pass in vector x and vector v (1D case) -- if you have 2 or more dimensions -- then the input coordinates must be in full gridded form, not individual samples. This can be done with griddata – below, we try out all of the interpolation methods: One can see that the exact result. pyplot as plt import numpy as np from scipy. Use griddedInterpolant to perform interpolation with gridded data. I want then to use those to create an interpolant where I can send new x,y values and get a z-value back. The subject line could equally well cite scatteredInterpolant as it shares the same underlying code as griddata. The size of the input v must match the size of the original data, either as a vector or a. v in the ScatteredInterpolant is just your data values at the x and y locations. This can be done either switching to a Interpreded MATLAB block or using coder. However, it is rather time consuming to perform the triangulation every time I use the file. 912 etc etc. "Warning: Duplicate data points have been detected and removed - corresponding values have been averaged. 5x0. This was executed as follows and provided good results, in that the interpolated Z points across the working XY grid looks like the shape I am expecting. Will parallel toolbox be helpful? Thanks. Installing No build system. Edited: Alexander Schwarzwälder on 23 Nov 2020. Closest coordinate points between two data sets. scatteredInterpolant giving null matrix. This means your matlab version has sample points at the positions U,V. scatteredInterpolant supports (x, y, v, then options, or (x, y, z, v, then options, so building an interpolation object over 2d or over 3d, that you then invoke with the appropriate number of input parameters to get results. I get the following warning from scatteredInterpolant. The points. scatteredInterpolant returns the interpolant F for the given data set. x = [1. When I did that step, command window shows " Requested 61890x61890 (28. Use scatteredInterpolant to perform interpolation on a 2-D or 3-D data set of scattered data . A scatteredInterpolant object F represents a surface of the form v = F(X). Generate a regular mesh from irregular data using interpolation. Prototyping at the command line may not yield the same level of performance. Learn more about scatteredinterpolant, fsolve Hi, I'm trying to implement solution of a nonlinear system, in which i'd like to use a scatteredInterpolant to calculate some values. TLDR: The Y and xq you've constructed work for scatteredInterpolant but not for griddedInterpolant which uses a different format. Unfortunately MATLAB does not have any scattered interpolation routines that work in more than 3 dimensions, but gridded interpolation can. If you have points which are described by vectors, and you want to plot them you could always use a Delauny triangulation. v in the ScatteredInterpolant is just your data values at the x and y locations. The 'linear' extrapolation method is based on a least-squares approximation of the gradient at the boundary of the convex hull. The choice of a specific interpolation routine depends on the data: whether it is one-dimensional, is given on a structured grid, or is unstructured. The interpolant uses monotonic cubic splines to find the value of new points. Here is an example: import matplotlib. Av = x (3)*x (4); % mm2 the web area when load is parallel to web. julia> ]add ScatteredInterpolation. bash-script scattered-data-interpolation. Use griddedInterpolant to perform interpolation. If z is a vector value, consider using interpn. What I have is a bunch of points (x,y,w), where x and y are coordinates and w is the value. I want to specify that scatteredInterpolant worked well in a script but not in the simulink function block. Creation of arrays greater than this limit may take a long time and cause MATLAB to become unresponsive. Besides splitting the creation of the object from the invocation for interpolation purposes, griddata simply does not. I tried to store the computed scatteredInterpolant objects for each time step in a cell array,. F = scatteredInterpolant (x_raw,y_raw,z_raw,'natural'); ZGrid = F (XGrid,YGrid); For my work it would be very useful to find the number of points from the raw data which fall into each element (pixel) of the resulting image (2D array). Just change the Values property of the scatteredInterpolant object to reference a different page of the zgrid variable each time you want to interpolate. My data consist on text files name from Output_00 to Output_23 in a folder. Scattered data, with some nasty stuff to interpolate on the edges, but still what appears to be a single valued relationship. You can evaluate F at a set of query points, such as (xq,yq) in. random(100) z = np. example. Vector x contains the sample points, and v contains the corresponding values, v ( x ). We know that we have some. Interpolation. . scatteredInterpolant returns the interpolant F for the given data set. The choice of a specific interpolation routine depends on the data: whether it is one-dimensional, is given on a structured grid, or is unstructured. 7e7). This mesh is equivalent to the bounding box for Alaska. Hello. The only difference in my code was just using:"scatteredInterpolant" Function Does. griddedInterpolant returns the interpolant F for the given data set. Assuming I have some scattered points; then I used scattered interpolant to having a 0. The usage is like this:I used scatteredInterpolant function to interpolate probability values all around the map. Interpolant surface fits use the MATLAB ® function scatteredInterpolant function for none, linear, and nearest neighbor extrapolation, and the MATLAB function griddata for biharmonic extrapolation. You don't have to actually have the function, F, just the points that correspond to the x and y data points given. Description. >> F = scatteredInterpolant(xdata, ydata, vals, 'natural' , 'none' );Have you seen the interp2 function?. Also, the integral2 function gives me "Warning: Non-finite result. I achieved this using cubic spline interpolation. interpolate. Thin-plate spline extrapolation uses the tpaps function, and PCHIP extrapolation uses the pchip function. However, it can only handle 2D and 3D scatter data, whereas this function can handle any number of dimensions. Use griddedInterpolant to perform interpolation with gridded data. scatteredInterpolant does a triangulation, and it is not uncommon for it to turn out that one of the three closest points to a given point can be from a different "layer" of Z. How to retain duplicate while using. Walter Roberson on 9 Dec 2015. La interpolación en MATLAB ® se divide en técnicas para puntos. One other factor is the desired smoothness of the interpolator. Updated on Apr 21, 2022. See the above example with nine points that represent four axis-parrallel elements. This is a follow up to an earlier question: what I have is a 4 column text file denoting a point cloud with one column denoting data that I use for color, and three column entries for x y and z coordinates. F = scatteredInterpolant (x_repeat,x1 (:,3)); %rather than throwing an error, shows a warning and cleans your data for you. You specify x and y as key / control points with the corresponding z and g output points. Sign in to answer this question. Use scatteredInterpolant to perform interpolation on a 2-D or 3-D data set of scattered data . This allows the object to continue using the same triangulation it built when it was originally constructed, which is a lot of the work involved in creating the object. libInterpolate is a header-only C++ library, so you can simply include the headers you want/need in your source code. 000 417826. random. I am asking about ways to view a 3D point cloud as surfaces. You can use scatteredInterpolant to do this for you. To use griddedinterpolant or interp2, a meshgrid or ndgrid needs to be created using lat, lon values. I have created a 2D contour map using a 25x19 matrix and was wondering how to interpolate the value at certain user-input x-y coordinates? Essentially, I want the user to enter coordinates that are either integer or decimal, and for the code to output the value at that corresponding location. >> F = scatteredInterpolant(xdata, ydata, vals, 'natural' , 'none' );scatteredInterpolant allows me to provide a set of input sampling positions and the corresponding sample values. Besides splitting the creation of the object from the invocation for interpolation purposes, griddata simply does not. " regardless of whether there's an extrapolation method . )Dear all, I had the value of precipitation in 93 scattered coordinate stations; I used "scatteredInterpolant" to interpolate this 93 scattered data in gridded coordinates. I am doing data interpolation using scatteredinterpolant method. Suppress Warnings. scatteredInterpolant is used to perform interpolation on a scattered dataset, which is basically what you have. 121444 0. scatteredInterpolant returns the interpolant F for the given data set. The MATLAB language is designed to give optimum performance when your application is structured into functions that reside in files. pwl_interp_2d_scattered , a C++ code which produces a piecewise linear interpolant to 2D scattered data, that is, data that is not guaranteed to lie on a regular grid. Accepted Answer: Voss. As listed below, this sub-package contains spline functions and classes, 1-D and multidimensional (univariate and multivariate) interpolation classes, Lagrange and Taylor polynomial interpolators, and wrappers for FITPACK and DFITPACK functions. Unfortunately MATLAB does not have any scattered interpolation routines that work in more than 3 dimensions, but gridded interpolation can. . The most similar command for data outside convex hull in octave to scatteredInterpolant of Matlab is griddata. Create a grid of 2-D sample points using ndgrid. 000 417826. The warning message returned by scatteredInterpolant reflects this fact. Step 2: constuct "V" of n by n matrix of velocity by rearranging the data. Interpolation (. 8sec, scatteredInterpolant: 10,1sec. Surf produces a pretty smooth surface, whereas with trisurf streaks start appearing. To use griddedinterpolant or interp2, a meshgrid or ndgrid needs to be created using lat, lon values. e. There will be some areas where you get garbage. Next, there is the issue of using noisy data to then be interpolated. Then I can query the interpolated values by supplying a set of positions: F = scatteredInterpolant(xpos, ypos, samplevals) interpvals = F(xgrid, ygrid) This is sort of the opposite of what I want. There is a high density of values scattered around in the center of the 3D space. Use scatteredInterpolant to perform interpolation on a 2-D or 3-D data set of scattered data . Features: Simple, consistent interface for all interpolators. x = sort (20*rand (100,1)); v = besselj (0,x); Create a gridded interpolant object for the data. See the syntax, input arguments, properties, and usage examples of this function in MATLAB. scatteredInterpolant returns the interpolant F for the given data set. griddedInterpolant 返回给定数据集的 插值 F 。. 208 1744. interpolate. scatteredInterpolant giving null matrix. Parameters. m script files are more advanced, providing data normalization before interpolation, and avoiding jumps in the plots. Extract your vertices data in a matrix. interpolate. . The sample points X must have size NPTS-by-2 in 2-D or NPTS-by-3 in 3-D, where NPTS is the number of points. 974 5333045. また、R2013a 以降では、グリッドデータに対しては griddedInterpolant 関数, 散布データに対しては、scatteredInterpolant 関数を使用することができます。. subroutine interp1 ( xData, yData, xVal, yVal ) ! Inputs: xData = a vector of the x-values of. It takes as input a set of scattered data points (x, y, z) and. griddedInterpolant evaluates each page in the 3-D image at. So I did, and found to be twice slower for a 512 by 512 matrix. That is, my data set consists from three vectors: X, Y, D. scatteredInterpolant returns the interpolant F for the given data set. interpn expects gridded data in a full grid format, which is not what your Y represents, at least in its current form. It is just presented as being v = F(x,y) because effectively that is what it is. griddata in this case, but you seem to want a callable interpolator,. The surface is always convex (as the name suggests)Use scatteredInterpolant to perform interpolation on a 2-D or 3-D data set of scattered data . 184942 0. I get the following warning from scatteredInterpolant. I would like to make a contour plot. Learn more about scatteredinterpolant: MATLAB the xyz data file consists out of 3157394 data triples like this: 417826. I have a geographically distributed data set with X-coordinate, Y-coordinate and corresponding target value of interest D. What I have is a matrix of x, y, z points that is my base data. It is possible to fit a single polynomial interpolant to data, with a degree one less than the number of data points. 0. scatteredInterpolant returns the interpolant F for the given data set. values ndarray of float or complex, shape (n,). See "lip" below":Similar to scatteredInterpolant (I guess) it uses delaunay tesselation and the user may choose among 3 algorithms: bilinear interpolation, sibson (default) and "non-sibsonian" interpolation. On the other hand, you indicate that you want to be able. Type erased AnyInterpolator container can hold each of the implemented interpolators. By default, griddedInterpolant uses the 'linear' interpolation method. scatteredInterpolant works perfectly with the syntax I used above, so thank you for this. A scattered data set is defined by sample points X and corresponding values v. I have compared the interpolation results using the tetrahedrals found from the TetGen and from the Matlab's own. The outer boundary surface of a Delaunay triangulation is in fact the convex hull of the data. Thin-plate spline extrapolation uses the tpaps function, and PCHIP extrapolation uses the pchip function. The function is defined by z = f (x, y). I have a big matrix M(100*10) and N(100*100). when I make mesh grid of x. However, before doing that, I created a mesh as a querry points. 您可以使用插值来填充缺失的数据、对现有数据进行平滑处理以及进行预测等。. 2 and z=0. Perl. Re: scatteredInterpolant. I was wondering if this process itself can be done in parallel processing because it takes VERY long for decently high resolutions (up to a hour for a 512x512x512 grid, which of course isn't trivial)I've written a code that uses TriScatteredInterp, but I read in Matlab's documentation that this will not be supported in future release and that I should instead use scatteredInterpolant. Use griddedInterpolant to perform interpolation with gridded data. Inputs x, y, z are vectors of the same length or x, y are vectors and z is. With these three matrices I created one surface, and than I got more three matrices to create another one. So I tried the scatteredInterpolant for it. For linear, do they mean a tangent plane approximation or a distance weighted approach? also for nearest, how can we know how many nearest neighbours are being used. currently griddata function was used for it which take much time and a warning to use scatteredInterpolant. I used scatteredInterpolant function to interpolate probability values all around the map. So I did, and found to be twice slower for a 512 by 512 matrix. One trick you can do is to add one number to the end the array to remove the collinear correlation. however, as scatteredInterpolant requires at least 2 dimensions for its indices, this doesn't work for 1d interpolation. Because the answer is not how to modify the plot AFTER you used scatteredInterpolant, but how to use the tool properly (or the proper tool) to produce a better result. LinearNDInterpolator(points, values, fill_value=np. A scattered data set defined by locations X and corresponding values V can be interpolated using a Delaunay triangulation of X. Extrapolating Scattered Data Factors That Affect the Accuracy of Extrapolation. . The Analytic, Interpolation, and Piecewise functions can also be added to Materials. 01 -160. However, before doing that, I created a mesh as a querry points. [new_lons,new_lats] =. Namely, scatteredInterpolant only offers nearest, linear, and natural interpolation Methods. Each text file consist on three columns, first is latitude, second is longitude and third is temperature. Your data lies in the plane (x1,y1,0). These tools work via triangulations of the domain - Delaunay triangulations, which result in convex things. pwl_interp_2d_scattered , a C++ code which produces a piecewise linear interpolant to 2D scattered data, that is, data that is not guaranteed to lie on a regular grid. –. The interpolation method can be "nearest", "cubic" or. The results always pass through the original sampling of the function. In the above code, x and y are linearly spaced vectors obtained from irregularly spaced raw data. In a previous discussion Kelly provided a means to convert a scattered vector to gridded. I tried it using "scatteredInterpolant", but the results were quite bad. However, it can only handle 2D and 3D scatter data, whereas this function can handle any number of dimensions. To my understanding about plotting a contour: step1: plot x and y according to grid size (n) required and draw a meshgrid. At first i have read the data from an excell sheet(. griddedInterpolant returns the interpolant F for the given data set. Find the treasures in MATLAB Central and discover how the community can help you! Start Hunting!ScatteredInterpolant just does what it is told, having no idea that when you try to interpolate some point in that volume, it is creating meaningless gibberish as a result. Parameters: points 2-D ndarray of floats with shape (n, D), or length D tuple of 1-D ndarrays with shape (n,). A brief explanantion of these functions is given below: griddata is a function in MATLAB that performs interpolation on scattered data to produce a grid. Both "griddata" and "scatteredInterpolant" can only interpolate data representing a single-valued function. I'm sorry, but you simply cannot use scatteredInterpolant to produce a meaningful result from this data, as you are trying to do. scatteredInterpolant 를 사용하여 2차원 또는 3차원 산점 데이터 의 데이터 세트에 보간을 수행합니다. This produces a surface of the form V = F (X). In a previous discussion Kelly provided a means to convert a scattered vector to gridded information, but it can potentially take up a lot of memory. However, the behavior of such fits is unpredictable between data points. % X1 X2 X3 X4 V. My understanding is that the underlying mechanisms behind MATLAB's scatteredInterpolant and python's griddata subpackage (from scipy. So even though your data happens to look non-convex, scatteredInterpolant does not care in the least. Thank you very much. It also looks like my interpolant to a regular grid isn't working?Hello, I am currently doing EEG traceability research, because I only have the subject’s EEG data and no MRI data, so I used the MRI template. values ndarray of float or complex, shape (n,). slx' (which uses the 'scatteredInterpolant' object created in MATLAB workspace) and MATLAB script 'scatterInterpolantObj. All of the input arguments "x", "y", and "v. griddedinterpolant expects points on a regular grid pretty much like interp2 - so that function seems unsuitable for your case. F = scatteredInterpolant (X,v) creates an interpolant that fits a surface of the form v = F (X) to the sample data set (X,v). The scatteredInterpolant class described in Interpolating Scattered Data Using the scatteredInterpolant Class is more efficient in this respect. scatteredInterpolant seems to do the job quite well for grid points within the boundaries of the original cloud; however, I still need the grid points falling outside the limits of the original dataset to be NaNs. Use griddedInterpolant to perform interpolation with gridded data. Francesc Purroy on 12 Nov 2018. Interpolation is interpolation. The plot is formed by joining adjacent points with straight lines. I have measured electric field data in three dimensions of the following form: Theme. Create a 10-by-10-by-10 grid of sample points. 000 417826. Hi, I am kind of struggling with scattered interpolation in Julia for 2D. The MATLAB language is designed to give optimum performance when your application is structured into functions that reside in files. Copy. The griddata function supports 2-D scattered data interpolation. interpolate. Learn how to use scatteredInterpolant to perform interpolation on a 2-D or 3-D data set of scattered data. Description. I have to interpolate the data in it. Use griddedInterpolant to perform interpolation with gridded data. a=3. If your scatter of points conforms fairly well to a cube shape, one approach could be to use griddata to interpolate onto a regular grid of data that fits within your point cloud (therefore avoiding nans) and then use this regular grid of values as the input to interpn which does facilitate linear extrapolation (but requires a regular grid as input). Based on your csv file, I am assuming you are trying to interpolate 2D data. scatteredInterpolant() on the. This discussion applies in any dimensionality. scatteredInterpolant を使用して、散布データの 2 次元または 3 次元データ セットの内挿を実行します。 scatteredInterpolant は指定したデータ セットの内挿 F を返します。 F をクエリ点の集合 (2 次元の (xq,yq) など) で評価して、内挿値 vq = F(xq,yq) を生成できます。Description. My scattered model data are 3 . So I have attempted to use scatteredInterpolant but it appears that this function appears to be not suited for this type of data, as it needs x, y, and a v (value) matrix, which is more dimensions than I have. 插值. Python bindings are also provided. ). eps= (235/fy)^ (1/2); % required for section classification. interpolate. interp(1D, 2D, 3D) In this article we will explore how to perform interpolations in Python, using the Scipy library. The support engineers are great, they really know how to choose a good subject line that will get a developer's attention and get a response back to the customer quickly. F = scatteredInterpolant(map. I haven't tried compiling or testing and my fortran may be a bit rusty, but something like the following should work. The scatteredInterpolant is doing its work using a 3-d tessellation. I am able to calculate the Delaunay tetrahedrals using the TetGen library. 9. GitHub is where people build software. 000 417826. You can evaluate F at a set of query points, such as (xq,yq) in 2-D, to produce interpolated values vq = F (xq,yq). You can evaluate F at a set of query points, such as (xq,yq) in 2-D, to produce interpolated values vq = F (xq,yq). The size of the input v must match the size of the original data, either as a vector or a. You can create the interpolant by calling scatteredInterpolant and passing the point. F= scatteredInterpolant(x,y,zi); contourf(X,Y,F(X,Y),100, 'LineColor', 'none') which is taking almost 3-4 minutes to plot a heatmap. Creation of arrays greater than this limit may take a long time and cause MATLAB to become unresponsive. My scattered data (sample: XS1 and XS2) have [x,y,z] values and appear as multiple lines. I post the resutls of the computational time: interp2:5. It is written in C, C++, Java and. The values in the y-matrix are strictly. The 'griddatan' function and 'scatteredInterpolant' object process the data differently, which leads to the difference in performance that you see. You can evaluate F at a set of query points, such as (xq,yq) in 2-D, to produce interpolated values vq = F (xq,yq). txt files which I import in the workspace in 3 column variables (no time dependency). cosmoscalibur. meshgrid(xi,yi. 98. You can evaluate F at a set of query points, such as (xq,yq) in 2-D, to produce interpolated values vq = F (xq,yq). The query points lie on a planar grid that is completely outside domain. The subject line could equally. There is no need to use griddata AFTER you used scatteredInterpolant! Here is your data. A scattered data set is defined by sample points X and corresponding values v. scatteredInterpolant 类支持二维和三维空间中的散点数据插值。可以通过调用 scatteredInterpolant，传递插值点位置和对应值，并使用内插和外插方法作为可选参数，来创建插值。有关可用于创建和计算 scatteredInterpolant 的语法的详细信息，请参阅 scatteredInterpolant 参考页。 This transforms the data so that the original mean μ becomes 0, and the original standard deviation σ becomes 1: x = ( x − μ) σ. This method fits smooth surfaces that also extrapolate well (for surfaces only). Use griddedInterpolant to perform interpolation.