MATLAB: How to find b spline values

bspline

Hello,

So I have some position data, I fitted a Bspline on the data and differentiate twice to get the accelerations. But now that I want to find the values of accelerations, I'm confused how to get that so I can divide them some number for normalization. So are the y values of a curve fitted by a bspline same as coefficients? I attached the spline, I need to find the y values of 101 points of this figure.

Best Answer

After computing the derivative

spline_position = spaps(time ,x,0,3);    % x is a 101 element vector  representing postion, I'm fitting a 5th order bspline 
acceleration = fnder(spline_position,2); % this gives me a struct, I  need to have a 101 acceleration vector corresponsing to each x

run this to evaluate the acceleration

a = fnval(acceleration, time)

Related Solutions

MATLAB: How to generate a spline interpolant that matches the derivative values in MATLAB 7.4 (R2007a)

This can be performed in MATLAB 7.4 (R2007a) using Hermite interpolation which is implemented in the function PWCH. The first few lines of the PWCH help read:

 PWCH Piecewise cubic Hermite interpolation
     PC = PWCH(X,Y,S) returns the ppform of the piecewise cubic Hermite
     interpolant f to the given data values Y and the given slopes S
     at the given data sites X. X must be a vector, and S must be of the same
     size as Y.

So, for example:

x = 1:10;
y = sin( x );
s = cos( x ); % slopes
xi = linspace( 0, 11, 491 );
pp = pwch( x, y, s ) 
plot( xi, ppval( pp, xi ), x, y, 'o', xi, pchip( x, y, xi ), '--' )

There is also this similar example in the user guide under Spline Toolbox -> Some Simple Examples -> Knot Choices

MATLAB: Condition for Specific Data collection

hello

see example below

this could be interesting for data 1 example

but the two other data it's not feasible unless someone come's with a clever condtion equation to select such fraction of data

 [num,txt,raw] = xlsread('Data 1.xlsx') ;
 
 time = num(:,1);       % s 
 current = num(:,2);    % A
 voltage = num(:,3);     % V
 
 samples = length(time);
 dt = (time(end)-time(1))/(samples-1);
 Fs = 1/dt;
 
 % main loop : extract min max vales for every 5 min data %
 [dvoltage, ddvoltage] = firstsecondderivatives(time,voltage);
figure(1);
subplot(2,1,1),plot(time,voltage,'-b');grid
subplot(2,1,2),plot(time,dvoltage,'-b');grid
% selected buffer is defined between the two positive peaks of dvoltage
dvoltage_max = max(dvoltage(dvoltage>0));
threshold = dvoltage_max/2;
ind = find(dvoltage > threshold);
ind_start = ind(1)-100;
ind_stop = ind(end)-100;
% plot selected portion of data
figure(2);
plot(time,voltage,'-b',time(ind_start:ind_stop),voltage(ind_start:ind_stop),'or');grid
function [dy, ddy] = firstsecondderivatives(x,y)
% The function calculates the first & second derivative of a function that is given by a set
% of points. The first derivatives at the first and last points are calculated by
% the 3 point forward and 3 point backward finite difference scheme respectively.
% The first derivatives at all the other points are calculated by the 2 point
% central approach.

% The second derivatives at the first and last points are calculated by
% the 4 point forward and 4 point backward finite difference scheme respectively.
% The second derivatives at all the other points are calculated by the 3 point
% central approach.
n = length (x);
dy = zeros;
ddy = zeros;
% Input variables:
% x: vector with the x the data points.
% y: vector with the f(x) data points.
% Output variable:
% dy: Vector with first derivative at each point.
% ddy: Vector with second derivative at each point.
dy(1) = (-3*y(1) + 4*y(2) - y(3)) / 2*(x(2) - x(1)); % First derivative
ddy(1) = (2*y(1) - 5*y(2) + 4*y(3) - y(4)) / (x(2) - x(1))^2; % Second derivative
for i = 2:n-1
   
dy(i) = (y(i+1) - y(i-1)) / 2*(x(i+1) - x(i-1));
ddy(i) = (y(i-1) - 2*y(i) + y(i+1)) / (x(i-1) - x(i))^2;
end
dy(n) = (y(n-2) - 4*y(n-1) + 3*y(n)) / 2*(x(n) - x(n-1));
ddy(n) = (-y(n-3) + 4*y(n-2) - 5*y(n-1) + 2*y(n)) / (x(n) - x(n-1))^2;
end

Best Answer

Related Solutions

MATLAB: How to generate a spline interpolant that matches the derivative values in MATLAB 7.4 (R2007a)

MATLAB: Condition for Specific Data collection

Related Question