Interpolating between end points in polar coordinates

I have an array of polarcoordinate pairs (r,theta), theta given in degrees

13.7807 208.5120

13.9924 225.4886

19.3740 232.1227

14.2353 261.4786

18.4920 282.1455

10.3117 298.3125

19.2983 306.1740

14.7913 326.8975

13.8365 342.4244

I want to interpolate to obtain an array of 360 r-values , one value for each integer degree around the circle.

I have applied the interp1-function to obtain the values:

theta = 1:360;

H = interp1(polarCoords(:,2),polarCoords(:,1),theta);

however I cannot obtain any values between 343 degrees and 208 degrees, H = nan for all angles between 343 and 208.

my questions are :

1 how can I obtain interpolating values between 343 degrees and 208 degrees?

2. I guess the interp1 does an linear interpolation in cartesian coordinates, meaning interpolating by straight lines between the points, if so, how can I interpolate following the curved coordinate line in polar coordinates (linear interpolation in polar coordinates) ?

Answer 1

[Star Strider]

Try this:

polcords = [13.7807  208.5120
            13.9924  225.4886
            19.3740  232.1227
            14.2353  261.4786
            18.4920  282.1455
            10.3117  298.3125
            19.2983  306.1740
            14.7913  326.8975
            13.8365  342.4244];


theta_new = linspace(0, 359.9, 360);
r_new = interp1(polcords(:,2), polcords(:,1), theta_new, 'linear', 'extrap');

polcords_new = [r_new(:) theta_new(:)];

figure
polarplot(deg2rad(polcords(:,2)), polcords(:,1), 'pg')
hold on
polarplot(deg2rad(polcords_new(:,2)), polcords_new(:,1), '-r')
hold off

It will do the interpolation (and extrapolation), however since it is simply extrapolating a line, not any sort of pattern, it simply plots a circle for the values it has no data how to to interpolate between. I used 'linear' here because other interpolation or extrapolation methods produced wildly divergent radii.

Experiment to get different results.

[Eirik Kvernevik]

thank you , its almost what I was looking for

but I would like the circle line to hit both the end points. Right now its starting at the endpoint at 208 degrees and ends at zero degrees. is it possible to cross the zero-degree line and connect it with the endpoint at 342 degrees ?

[Star Strider]

Yes, although the interpolation method you choose depends on the result you want.

Try this:

r_new = interp1(polcords(:,2), polcords(:,1), theta_new, 'nearest', 'extrap');

Experiment with other interpolation methods to get different results.

[Eirik Kvernevik]

cool, thanks mate !

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

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