1) Generate intermediate points in a set of X,Y while respecting the original points order. 2) Generate same number of points for 2 different set of X,Y with different sizes.

1) Generate intermediate points in a set of X,Y in matlab while respecting the original points order.

2) Generate same number of points for 2 different set of X,Y with different sizes.

I hope my question is clear.

Imagine I have 2 variables with totaly different sizes :

a=[2,1;2,2;1,4;-1,4;-2,1;-2,-2;0,-3;1.5,0];
b = [3,2;3,3;2,5;0,6;-2,5;-3,2;-3,-1;0,-4;2,-2];

I need to generate 2 variables of same dimensions (say 1000 points, Equidistant) from a and b. the first strating with a-start and the second with b-start.

3) I have something like this in 3D but hope an idea to do it for 2D will work also for 3D

Thank you

[Mathieu NOE]

hello

i am not 100% if you want to interpolate each curve separately , or create a interpolated curve between a and b curves (would need to resample both with same number of points)

[Mohamad TOUT]

Hi,

I want a kind of interpolation of each curve separately.

The idea of resampling both curve should be based on same number of points and the starting points of each original curve.

[Mathieu NOE]

As always , my pleasure !

and we should also warmly thanks @John D'Errico for his marvelous Fex submissions

Answer 1

[Mathieu NOE]

my turn to try something... with the help of interparc :

interparc - File Exchange - MATLAB Central

NB that nothing forces the two curves to be parallel (otherwise it would be better to start with a central line and then create the two "borders")

try with the different interpolation methods and pick the one you prefer

here also I took only N = 100 points so we can clearly see them on the plot, but you can opt for more if you want..

may I also point out that going from a very low sampling like 8 points to 1000 interpolated points leaves a lot or room to "interpret" what shape you want to follow (linear, polynomial - which order ?)

a=[2,1;2,2;1,4;-1,4;-2,1;-2,-2;0,-3;1.5,0];
b = [3,2;3,3;2,5;0,6;-2,5;-3,2;-3,-1;0,-4;2,-2];
plot(a(:,1),a(:,2),'ro','markersize',20);grid
hold on
plot(b(:,1),b(:,2),'gs','markersize',20),grid

% interpolate using parametric splines
N = 100;
pta = interparc(N,a(:,1),a(:,2),'pchip');
ptb = interparc(N,b(:,1),b(:,2),'pchip');

% Plot the result
plot(pta(:,1),pta(:,2),'r-*');
plot(ptb(:,1),ptb(:,2),'g-*');
hold off
grid on
axis equal

[John D'Errico]

If the goal is equidistant points along an arc, interparc is the right tool. And it works in any number of dimensions. Of course, I may be biased. ;-)

[Mohamad TOUT]

Thank you so much, Mathieu.

Thanks to all of you. This is exactly what I was looking for.

The results in my case study are truly surprising!

Answer 2

[Alan Stevens]

Something like this? (I've just used 50 interpolated points for clarity below). Choose your own interpolation type. The "equidistant" below is interpreted as equal angle separation.

a=[2,1;2,2;1,4;-1,4;-2,1;-2,-2;0,-3;1.5,0];
b = [3,2;3,3;2,5;0,6;-2,5;-3,2;-3,-1;0,-4;2,-2];
plot(a(:,1),a(:,2),'ro-',b(:,1),b(:,2),'bs-'),grid
hold on

% convert to polar coordinates
[tha,ra] = cart2pol(a(:,1),a(:,2));
[thb,rb] = cart2pol(b(:,1),b(:,2));
tha(tha<=0)=tha(tha<=0)+2*pi;
thb(thb<=0)=thb(thb<=0)+2*pi;
na = length(tha);
nb = length(thb);

n = 50;  % Nbr of interpolated points
i = 1:n;
thetaa(i) = (tha(na)-tha(1))*(i-1)/(n-1) + tha(1);
thetab(i) = (thb(nb)-thb(1))*(i-1)/(n-1) + thb(1);
xa = interp1(tha,a(:,1),thetaa);
ya = interp1(tha,a(:,2),thetaa);
xb = interp1(thb,b(:,1),thetab);
yb = interp1(thb,b(:,2),thetab);

plot(xa,ya,'*:',xb,yb,'+:')

[Mathieu NOE]

I wonder if the OP wanted something like a spline interpolation, and with equidistant with ds = sqrt(dx²+dy²) in mind ?

[Mohamad TOUT]

Thanks for this idea.

but unfortunately this will no work for me. Maybe I gave a wrong data set as example.

Just try to add one point (outside the circle) at the end of b for example : 4,4. Then the interp1 will not work anymore.

//// Please imagine this problem like a F1 track with both set of points are the left and right side of the track :) \\\\