Extrapolated scatter data

Catalog

Factors affecting the accuracy of extrapolation

Compare the extrapolation of coarse sampling and fine sampling scatter data

3D data extrapolation

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Factors affecting the accuracy of extrapolation

        scatteredInterpolant It provides the function of finding approximate solutions to points outside the convex hull .'linear' The extrapolation method is based on the least square approximation of the gradient at the convex hull boundary . The value returned for the query point outside the convex hull is based on the value at the boundary and the gradient . The quality of the solution depends on the way the data is sampled . If it is rough data sampling , The quality of extrapolation is poor .

         Besides , Triangulation near the convex hull boundary may have strip triangles . These triangles will affect the extrapolation results , It will affect the interpolation results . The extrapolation results should be visually checked with knowledge of the external behavior of the domain .

Compare the extrapolation of coarse sampling and fine sampling scatter data

         This example shows how to insert two different samples of the same parabolic function . This example shows that a better distribution of sampling points can produce better extrapolation results .

around 10 Concentric circles are created with a spacing of 10 Radial distribution point of degree . Use bsxfun Calculate the coordinate x=cosθ and y=sinθ.

theta = 0:10:350;
c = cosd(theta);
s = sind(theta);
r = 1:10;

x1 = bsxfun(@times,r.',c);
y1 = bsxfun(@times,r.',s);

figure
plot(x1,y1,'*b')
axis equal

         As shown in the figure ：

         Create a second set of points with a coarser distribution . Use rand Function in range [-10, 10] Create random samples in . 

rng default;
x2 = -10 + 20*rand([25 1]);
y2 = -10 + 20*rand([25 1]);
figure
plot(x2,y2,'*')

         As shown in the figure ：

         Parabola function at two point sets v(x,y) sampling . 

v1 = x1.^2 + y1.^2;
v2 = x2.^2 + y2.^2;

         in the light of v(x,y) For each sample created scatteredInterpolant.

F1 = scatteredInterpolant(x1(:),y1(:),v1(:));
F2 = scatteredInterpolant(x2(:),y2(:),v2(:));

         Create a grid of query points that will extend outside each domain .

[xq,yq] = ndgrid(-20:20);

         Calculation F1 And draw the results .

figure
vq1 = F1(xq,yq);
surf(xq,yq,vq1)

         As shown in the figure ：

         Calculation F2 And draw the results . 

figure
vq2 = F2(xq,yq);
surf(xq,yq,vq2)

         As shown in the figure ：

         Due to v2 The points in are roughly sampled ,F2 The extrapolation quality of is poor . 

3D data extrapolation

         This example shows how to use  scatteredInterpolant  Extrapolate the well sampled 3D mesh dataset . The query point is located on a flat grid completely outside the domain .

         Create a 10×10×10 grid . The points in each dimension are in the range [-10, 10] in .

[x,y,z] = ndgrid(-10:10);

         The function at the sampling point v(x,y,z) sampling .

v = x.^2 + y.^2 + z.^2;

         establish scatteredInterpolant, And specify linear interpolation and extrapolation .

F = scatteredInterpolant(x(:),y(:),z(:),v(:),'linear','linear');

         Calculation x-y Grid midspan [-20,20] Range and elevation is z =15 Interpolation of time .

[xq,yq,zq] = ndgrid(-20:20,-20:20,15);
vq = F(xq,yq,zq);
figure
surf(xq,yq,vq)

         As shown in the figure ：

         Because the function is well sampled , Extrapolation returns better results .