Define some sample points and calculate the value of a trigonometric function at those locations. These points are the sample values for the interpolant.

t = linspace(3/4*pi,2*pi,50)'; x = [3*cos(t); 2*cos(t); 0.7*cos(t)]; y = [3*sin(t); 2*sin(t); 0.7*sin(t)]; v = repelem([-0.5; 1.5; 2],length(t));

Create the interpolant.

F = scatteredInterpolant(x,y,v);

Evaluate the interpolant at query locations (xq,yq).

tq = linspace(3/4*pi+0.2,2*pi-0.2,40)'; xq = [2.8*cos(tq); 1.7*cos(tq); cos(tq)]; yq = [2.8*sin(tq); 1.7*sin(tq); sin(tq)]; vq = F(xq,yq);

Plot the result.

plot3(x,y,v,'.',xq,yq,vq,'.'), gridontitle('Linear Interpolation') xlabel('x'), ylabel('y'), zlabel('Values') legend('Sample data','Interpolated query data','Location','Best')

Create an interpolant for a set of scattered sample points, then evaluate the interpolant at a set of 3-D query points.

Define 200 random points and sample a trigonometric function. These points are the sample values for the interpolant.

rngdefault; P = -2.5 + 5*rand([200 3]); v = sin(P(:,1).^2 + P(:,2).^2 + P(:,3).^2)./(P(:,1).^2+P(:,2).^2+P(:,3).^2);

Create the interpolant.

F = scatteredInterpolant(P,v);

Evaluate the interpolant at query locations (xq,yq,zq).

[xq,yq,zq] = meshgrid(-2:0.25:2); vq = F(xq,yq,zq);

Plot slices of the result.

xslice = [-.5,1,2]; yslice = [0,2]; zslice = [-2,0]; slice(xq,yq,zq,vq,xslice,yslice,zslice)

Replace the elements in theValuesproperty when you want to change the values at the sample points. You get immediate results when you evaluate the new interpolant because the original triangulation does not change.

Create 50 random points and sample an exponential function. These points are the sample values for the interpolant.

rng('default') x = -2.5 + 5*rand([50 1]); y = -2.5 + 5*rand([50 1]); v = x.*exp(-x.^2-y.^2);

Create the interpolant.

F = scatteredInterpolant(x,y,v)

F = scatteredInterpolant with properties: Points: [50x2 double] Values: [50x1 double] Method: 'linear' ExtrapolationMethod: 'linear'

Evaluate the interpolant at(1.40,1.90).

F(1.40,1.90)

ans = 0.0069

Change the interpolant sample values and reevaluate the interpolant at the same point.

vnew = x.^2 + y.^2; F.Values = vnew; F(1.40,1.90)

ans = 5.6491

Usegroupsummaryto eliminate duplicate sample points and control how they are combined prior to callingscatteredInterpolant.

Create a 200-by-3 matrix of sample point locations. Add duplicate points in the last five rows.

P = -2.5 + 5*rand(200,3); P(197:200,:) = repmat(P(196,:),4,1);

Create a vector of random values at the sample points.

V = rand(size(P,1),1);

If you attempt to usescatteredInterpolant重复采样点,它会抛出一个警告and averages the corresponding values inVto produce a single unique point. However, you can usegroupsummaryto eliminate the duplicate points prior to creating the interpolant. This is particularly useful if you want to combine the duplicate points using a method other than averaging.

Usegroupsummaryto eliminate the duplicate sample points and preserve the maximum value inVat the duplicate sample point location. Specify the sample points matrix as the grouping variable and the corresponding values as the data.

[V_unique,P_unique] = groupsummary(V,P,@max);

Since the grouping variable has three columns,groupsummaryreturns the unique groupsP_uniqueas a cell array. Convert the cell array back into a matrix.

P_unique = [P_unique{:}];

Create the interpolant. Since the sample points are now unique,scatteredInterpolantdoes not throw a warning.

I = scatteredInterpolant(P_unique,V_unique);

Compare the results of several different interpolation algorithms offered byscatteredInterpolant.

Create a sample data set of 50 scattered points. The number of points is artificially small to highlight the differences between the interpolation methods.

x = -3 + 6*rand(50,1); y = -3 + 6*rand(50,1); v = sin(x).^4 .* cos(y);

Create the interpolant and a grid of query points.

F = scatteredInterpolant(x,y,v); [xq,yq] = meshgrid(-3:0.1:3);

Plot the results using the'nearest','linear', and'natural'方法。每一次插值方法改变s, you need to requery the interpolant to get the updated results.

F.Method ='nearest'; vq1 = F(xq,yq); plot3(x,y,v,'mo') holdonmesh(xq,yq,vq1) title('Nearest Neighbor') legend('Sample Points','Interpolated Surface','Location','NorthWest')

F.Method ='linear'; vq2 = F(xq,yq); figure plot3(x,y,v,'mo') holdonmesh(xq,yq,vq2) title('Linear') legend('Sample Points','Interpolated Surface','Location','NorthWest')

F.Method ='natural'; vq3 = F(xq,yq); figure plot3(x,y,v,'mo') holdonmesh(xq,yq,vq3) title('Natural Neighbor') legend('Sample Points','Interpolated Surface','Location','NorthWest')

Plot the exact solution.

figure plot3(x,y,v,'mo') holdonmesh(xq,yq,sin(xq).^4 .* cos(yq)) title('Exact Solution') legend('Sample Points','Exact Surface','Location','NorthWest')

Query an interpolant at a single point outside the convex hull using nearest neighbor extrapolation.

Define a matrix of 200 random points and sample an exponential function. These points are the sample values for the interpolant.

rng('default') P = -2.5 + 5*rand([200 2]); x = P(:,1); y = P(:,2); v = x.*exp(-x.^2-y.^2);

Create the interpolant, specifying linear interpolation and nearest neighbor extrapolation.

F = scatteredInterpolant(P,v,'linear','nearest')

F = scatteredInterpolant with properties: Points: [200x2 double] Values: [200x1 double] Method: 'linear' ExtrapolationMethod: 'nearest'

Evaluate the interpolant outside the convex hull.

vq = F(3.0,-1.5)

vq = 0.0029

禁用外推和评估Fat the same point.

F.ExtrapolationMethod ='none'; vq = F(3.0,-1.5)

vq = NaN