interpViaDistance

Interpolation via weighting of reciprocal distance

Contents

Syntax

Description

out=interpViaDistance(x, sampleInput, sampleOutput) returns the interpolated value based on sampleInput and sampleOutput, using weighting factors of reciprocal distance.

• x: an input matrix whose output values are to be computed
• sampleInput: sample input matrix where each column is a known data instance
• sampleOutput: a vector of corresponding output values
• finalOutput: interpolated output values corresponding to x

Example

1D example

sampleInput=[1 2 3 5 7 6];
sampleOutput=[3 5 6 7 8 7.5];
x=linspace(min(sampleInput), max(sampleInput));
y=0*x;
for i=1:length(y);
	y(i)=interpViaDistance(x(i), sampleInput, sampleOutput);
end
plot(sampleInput, sampleOutput, 'o', x, y);
legend('Sample data', 'Interpolated curve', 'Location', 'SouthEast');

2D example

sampleData=[0 3 4; 1 4 2; 3 1 6; 2 4 3; 4 2 1; 2 3 1; 4 4 0];
sampleInput=[0 1 3 2 4 2 4;3 4 1 4 2 3 4];
sampleOutput=[4 2 6 3 1 1 0];
pointNum=20;
x=linspace(min(sampleInput(1,:)), max(sampleInput(1,:)), pointNum);
y=linspace(min(sampleInput(2,:)), max(sampleInput(2,:)), pointNum);
z=zeros(length(x), length(y));
for i=1:length(x)
	for j=1:length(y)
		z(j,i)=interpViaDistance([x(i); y(j)], sampleInput, sampleOutput);
	end
end
figure; mesh(x, y, z);
h=line(sampleInput(1,:), sampleInput(2,:), sampleOutput, 'marker', 'o', 'linestyle', 'none');
xlabel('X'); ylabel('Y'); zlabel('Z');
title('Interpolated surface');
view(120, 20);
box on
rotate3d on
axis tight

See Also

interpViaGaussian.

Published with MATLAB® R2018a