Creation of new waypoints between existing waypoints

Hi, I am working on a path following project. I managed to create a serie of waypoints WP=((x1,y2) (x2,y2) ... (xn,yn)) and results of path following are already satisfying. But I would to create new waypoints between existing waypoints for better results.

Note that coordinates can be positive or negative and x coordinates are not necessarily increasing.

This image is an example. Red points are existing waypoints and I begin to draw in blue new waypoints I would like to create.

Thanks for your help

Answer 1

[the cyclist]

You are not giving us very much info to go on here. But perhaps using the interp1 function to interpolate, possibly using a spline?

[Thomas LHOMME]

Thanks for answering quickly. Here is my list of waypoints. I would like to create new waypoints and to choose the spacing between them. I cannot use interp1 because for this function x must be strictly increasing. And I do not want to create a step of time to use spline. Is there other option ?

Answer 2

[darova]

Try this

    % parameter - curve length
t = [0; cumsum(sqrt(diff(x).^2+diff(y).^2))];
    % refine parameter
t1 = linspace(0,t(end));
xt = spline(t,x,t1);
yt = spline(t,y,t1);
plot(x,y,'o-r')                % original data
hold on
plot(xt,yt)                    % interpolated data
hold off

[Thomas LHOMME]

I tried and modified it, but it does not worked...

[darova]

Too sad. Maybe another time?

[the cyclist]

This solution worked nicely for me, but I had to change

t = [0; cumsum(sqrt(diff(x).^2+diff(y).^2))];

to

t = [0 cumsum(sqrt(diff(x).^2+diff(y).^2))];

because I used x and y as row vectors.

Answer 3

[the cyclist]

In that case, you could do piecewise interpolation. If linear interpolation is fine, then this will work:

numOrigPts = numel(x);
numWayPts = 5;

xx = zeros(numWayPts*(numOrigPts-1),1);
yy = zeros(numWayPts*(numOrigPts-1),1);

for np = 1:numOrigPts-1
    xint = (x(np+1)-x(np))/(numWayPts+1);
    xx(numWayPts*(np-1)+1:numWayPts*np) = x(np) + xint*(1:numWayPts);
    yint = (y(np+1)-y(np))/(numWayPts+1);
    yy(numWayPts*(np-1)+1:numWayPts*np) = y(np) + yint*(1:numWayPts);
end

figure
hold on
plot(x,y,'*')
plot(xx,yy,'+')

where x and y are your original data. (Note that I have essentially recreated linear interpolation manually. I did this because you need to calculate the intervening x regardless, so doing the y values as well is exactly the same.)

But I think that @darova's solution is superior to this one, for making a smooth path around. See my comment there. However, mine has the advantage of creating equal numbers of waypoints between each original point, if that is important to you.