comparing consecutive coordinate values in terms of X , Y and Z.

I am trying to compare the consecutive values of centroid(points generated randomly : p = rand(100,3)) in all the three axes individually so as the change in values of consecutive coordinates in any particular axes value leads me to velocity in that particular axes(by using a formula to relate distance with time).Then i wish to find the acceleration from that velocity value so that i have the axis of change in acceleration as well.

Any expert guidance with a descriptive explanation would be appreciated.

[madhan ravi]

upload your code and required datas and illustrate an example onto where your getting at

Answer 1

[KSSV]

N = 100; 
P = rand(N,3) ;
% Get distances 
d = pdist2(P,P) ;
[Q,idx] = sort(d(:,1)) ;  % arrange points according to nearest 
P = P(idx,:) ;

[Pratik Pandya]

The solution provided is okay when we sort the values in increasing order.But we want it to be random so as to show the effectiveness of the program as we want a code to be executed in a loop which checks the x , y and z coordinate of a set of random values in every iteration and based on that we want the related change in coordinate , magnitude of coordinate changed, velocity of the change in the coordinates in that axis and related acceleration.

[KSSV]

For a given point....which point you want to pick? What's the criteria?

[Pratik Pandya]

I am trying to generate the points to be called as centroid of the object in (x,y,z). Now the change between any two consecutive values in x , y or z should lead me to velocity (change in that particular coordinate by time) in that particular direction in a loop.

ex: Centroid changes from A (10 , 20 ,30) to B(10,30,30)in 5 seconds and then to C (20,30,30) in another 5 seconds. in this condition , we see there is a change in the y coordinate. So by anyway can we calculate the velocity in this condition??

[KSSV]

Get the distance and divide it by the time....That's why I have calculated distance in the given code.

[Pratik Pandya]

but i am confused as to how to assign the x , y and z coordinates. the distance that you measured is okay but i want the specific coordinate that has the change, so that i can dedicate it to change in the that particular axis. and then using the formulae to calculate the acceleration and then eventually force , all depends on the direction.

[KSSV]

Huumh....so in that case, you need to have a criteria on how the path is going to be, given a initial condition/ point. So by this criteria, you have to keep on adding path or points. Isn't it?

[Pratik Pandya]

yes.we can assign the initial point coordinates but as we are planning to track the force values associated with the change in the object's position.Therefore we are planning to generate a random allotment(path) where the coordinates can change in an indefinite manner or random path.

can you please guide me in this case?

[KSSV]

P0 = rand(3,1) ;
N = 100 ;
P = zeros(N,3) ;
P(1,:) = P0 ;
for i = 2:100
    x = rand ; y = rand ; z = rand ;
    % decide the condition 
    % Along x 
    if x > 0.5 
        P(i,1) = P(i-1,1)+0.5 ;
    else
        P(i,1) = P(i-1,1) ;
    end
    % Along y 
    if y < 0.5 
        P(i,2) = P(i-1,2)+0.5 ;
    else
        P(i,2) = P(i-1,2) ;
    end
    % Along z
    if z > 0.5 
        P(i,3) = P(i-1,3)+1 ;
    else
        P(i,3) = P(i-1,3) ;
    end
    plot3(P(1:i,1),P(1:i,2),P(1:i,3))
    drawnow
end

There could be many other ways..depends. Have a look on random walk problem once.

[Pratik Pandya]

sure. I will work more on it and let you know. This seems okay to me as of now.

Thanks a lot.

[KSSV]

Thanks is accepting answer..:)

[Pratik Pandya]

But i have not exactly accepted this answer to be true unless i work on it.

[KSSV]

Ha ha..that's fine....

[Pratik Pandya]

Can you explain me this code please? KSSV?

[Pratik Pandya]

Let us say we have fixed starting and ending point of the path. But the intermediate points are randomly selected.Now after every time interval (can be frequency also , if it is effective), the change in each coordinate ( in terms of x or y or z) from the previous value should be compared so as to know the distance travelled and the direction as well.once we have the distance covered (and the axis where the coordinate change is observed) we have to find the velocity to show the velocity increase in that direction (x or y or z).and then i want to calculate the acceleration from the velocity values.

[KSSV]

It is simple right? If A(X1,y1,z1) point is changed to B(X2,y2,z2). Then velocity is given by:

((x2-x1)/dt,(y2-y1)/dt,(z2-z1)/dt).