Interpolation

Andrea86 · Oct 5, 2012

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

IRstuff · Oct 5, 2012

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?

TTFN
faq731-376

LiteYear · Oct 8, 2012

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:

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:

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

Code:

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

Eng-Tips is the largest engineering community on the Internet

Intelligent Work Forums for Engineering Professionals

Interpolation

Andrea86

Bioengineer

Recommended for you

IRstuff

Aerospace

LiteYear

Computer

Similar threads

Part and Inventory Search

Sponsor