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# Interpolation

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## Interpolation

(OP)
Hello everyone,
I need to interpolate a trajectory.
The trajectory is an array with the X and Y coordinates. The problem is that, since it is not a function, there are more that one Y value for each X and vicecersa.
For example:
Trajectory:
[1 4
2 5
3 6
4 8
5 10
6 11
7 12
9 11
10 9
9 8
8 7
7 6
7 5
8 5
9 4
11 4
12 4]
I tried to use the function interp1 but it gives me an error because my trajectory is not a function.
Since the position is stored with a frequency of 14 Hz, I have lost some information of the path. This is why I need an interpolation.
Moreover I have also multiple X for the same Y. It means that transpose the X with the Y doesn't help.
How can I do it?
There is a function that interpolates trajectory and not only function?
Is there any function in Matlab that allows me to interpolate vectors?
Thanks in advance to everyone
Andrea

### RE: Interpolation

Your biggest issue is going to be that linear interpolation will suck at accurately predicting the estimated trajectory. Your data shows lots of turns, which I assume were originally smooth changes in direction?

Are these points sufficiently accurate to use for a spline fit?

### RE: Interpolation

Interesting issue that surprisingly doesn't seem solved in the various forums. Would seem to me to be a FAQ when using interp1. Anyway, after a bit of playing I have a solution.

As you say, interp1 and friends won't do non-functions, so you need to generate an equivalent function by parameterising. By using a simple parameterisation on both the X and Y points, you get two functions that can be independently interpolated. De-parameterisation will then give you the interpolation of the original non-function.

#### CODE --> matlab

XY = <paste data from original post>;
X = XY(:, 1);
Y = XY(:, 2);
t = 0:0.1:17;
X1 = interp1(1:17,X,t);
Y1 = interp1(1:17,Y,t);
plot(X,Y,'o', X1,Y1,'-') 

Now as IRstuff goes on to say, maybe a linear interpolation is not ideal. Good news is that other interpolation functions slot right in:

#### CODE --> matlab

X1 = pchip(1:17,X,t);
Y1 = pchip(1:17,Y,t);
plot(X,Y,'o', X1,Y1,'-') 

#### CODE --> matlab

X1 = spline(1:17,X,t);
Y1 = spline(1:17,Y,t);
plot(X,Y,'o', X1,Y1,'-') 

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