Interpolation using B-spline or Nurbs

Hi

I have three data sets inside a circle of radius 3m (Fig & data attached). I want to obtain the following two results

1. To make closed curve for each data set using spline or Nurbs.
2. To interplotate a number of such curves i.e. let say 10 such closed curve btw red & purple data set and 10 curve btw purple & green data set.

Please suggest how to do this interpolation using spline or nurbs

Answer 1

[Vinayak]

Hi Mukesh,

The provided data can be used to create three sets of points: green, purple, and red.

I ensured that the points form a closed shape, typically by setting the final value as the first value:

function points = ensure_closed(points) 
if points(:,1) ~= points(:,end) 
    points(:,end+1) = points(:,1); 
end 
end 

Next, we need to determine the shape of the curve using splines. Here, I used a specific number of points(adjust for smoothness) to be generated along the expected spline:

function splinePoints = interpolateShape(shape, numPoints) 
t = linspace(1, length(shape), length(shape)); 
tt = linspace(1, length(shape), numPoints); 
xx = spline(t, shape(1,:), tt); 
yy = spline(t, shape(2,:), tt); 
splinePoints = [xx; yy]; 
end 

Once you have the splines for all three sets, we can interpolate between each pair to get the interpolated curves between them:

function interpolateBetweenShapes(shape1, shape2, numInterpolations) 
colors = jet(numInterpolations); % Colormap for interpolated shapes 
for i = 1:numInterpolations 
    alpha = i / (numInterpolations + 1); 
    interpolatedShape = (1-alpha) * shape1 + alpha * shape2; 
    plot(interpolatedShape(1,:), interpolatedShape(2,:), '-', 'Color', colors(i,:), 'LineWidth', 1.5); 
end 
end 

I plotted the result for the green and purple points, and this results in:

Similarly, we can generate the data between the other set of points.