Hello,
i want to know how scatteredinterpolant calculates query points that lie on the convex hull of the sample points.
I need to know this specifically for natural neighbor interpolation. To my understanding points on the convex hull produce unbounded voronoi cells with an infinite area, which means that all weights used for the interpolation should be zero (since the weights are defined as overlapping area devided by the area of the new voronoi cell), which in return means no interpolation is possible.
The interpolation is tested with the following code. The value of qv is returned as 0.5484.
Points=[-1.5 3.2; 1.8 3.2; -3.7 1.5; -1.5 1.3;
0.8 1.2; 3.3 1.5; -4.0 -1.0; -2.3 -0.7;
0 -0.5; 2.0 -1.5; 3.7 -0.8; -3.5 -2.9;
-0.9 -3.9; 2.0 -3.5; 3.5 -2.25];
z=Points(:,2).*sin(Points(:,1)) – Points(:,1).*cos(Points(:,2));
qP=[0.3 3.2];
F = scatteredInterpolant(Points(:,1),Points(:,2),z);
F.Method = ‘natural’;
qv=F(qP);

figure(1)
voronoi(Points(:,1),Points(:,2));

figure(2)
AllPoints=[Points; qP];
voronoi(AllPoints(:,1),AllPoints(:,2));Hello,
i want to know how scatteredinterpolant calculates query points that lie on the convex hull of the sample points.
I need to know this specifically for natural neighbor interpolation. To my understanding points on the convex hull produce unbounded voronoi cells with an infinite area, which means that all weights used for the interpolation should be zero (since the weights are defined as overlapping area devided by the area of the new voronoi cell), which in return means no interpolation is possible.
The interpolation is tested with the following code. The value of qv is returned as 0.5484.
Points=[-1.5 3.2; 1.8 3.2; -3.7 1.5; -1.5 1.3;
0.8 1.2; 3.3 1.5; -4.0 -1.0; -2.3 -0.7;
0 -0.5; 2.0 -1.5; 3.7 -0.8; -3.5 -2.9;
-0.9 -3.9; 2.0 -3.5; 3.5 -2.25];
z=Points(:,2).*sin(Points(:,1)) – Points(:,1).*cos(Points(:,2));
qP=[0.3 3.2];
F = scatteredInterpolant(Points(:,1),Points(:,2),z);
F.Method = ‘natural’;
qv=F(qP);

figure(1)
voronoi(Points(:,1),Points(:,2));

figure(2)
AllPoints=[Points; qP];
voronoi(AllPoints(:,1),AllPoints(:,2)); Hello,
i want to know how scatteredinterpolant calculates query points that lie on the convex hull of the sample points.
I need to know this specifically for natural neighbor interpolation. To my understanding points on the convex hull produce unbounded voronoi cells with an infinite area, which means that all weights used for the interpolation should be zero (since the weights are defined as overlapping area devided by the area of the new voronoi cell), which in return means no interpolation is possible.
The interpolation is tested with the following code. The value of qv is returned as 0.5484.
Points=[-1.5 3.2; 1.8 3.2; -3.7 1.5; -1.5 1.3;
0.8 1.2; 3.3 1.5; -4.0 -1.0; -2.3 -0.7;
0 -0.5; 2.0 -1.5; 3.7 -0.8; -3.5 -2.9;
-0.9 -3.9; 2.0 -3.5; 3.5 -2.25];
z=Points(:,2).*sin(Points(:,1)) – Points(:,1).*cos(Points(:,2));
qP=[0.3 3.2];
F = scatteredInterpolant(Points(:,1),Points(:,2),z);
F.Method = ‘natural’;
qv=F(qP);

figure(1)
voronoi(Points(:,1),Points(:,2));

figure(2)
AllPoints=[Points; qP];
voronoi(AllPoints(:,1),AllPoints(:,2)); interpolation, scatteredinterpolant, convex hull, voronoi, natural neighbor interpolation MATLAB Answers — New Questions

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