2D approximation with B-Splines

Currently I am working on a script to run a approximation with B-Splines using the de Boor's algorithm.

So I scripted the mathematical functions from:

http://www.tm-mathe.de/Themen/html/funbezierbspline.html

For getting started I tried to approximate a trepezoid using the control points:

and

It seems that my code works well (picture 1) but when I add more control points,

the results are strange (picture 2).

and

This is my function:

function s = f_Bspline(Cx, Cy, m)
% Calculation of B-Spline
% Cx, Cy: Control points
% m: Polynomal degree

%% Parameters

% Calculate amount of control points 
% Control points: n + 1
n = size(Cx,2) - 1;

% Plot intervall
t = 0:0.01:n-m+1;


%% Calculate knot vector

% Knot vector T
T = [];
for j=0:1:n+m+1
    if j <= m
        a = 0;
    elseif j >= m+1 && j <= n
        a = j - m;
    elseif j > n
        a = n - m + 1;
    end
    T(j+1) = a;
end

%% Calculate splines

% Spline Matrx
% s(1,:) : x values
% s(2,:) : y values
s = zeros(2, size(t,2));

% Calculate B-Spline for all t
for z=1:1:size(t,2)
    % s(1,z) = Sum { x_i * B_i,m(t) }, i = 0,1, ... ,n
    % s(2,z) = Sum { y_i * B_i,m(t) }, i = 0,1, ... ,n
    s(1,z) = 0;
    s(2,z) = 0;
    for i=0:1:n
        % Calculate B-Spline
        Bspl = f_BsplineBase(i, m, t(z), T);
        % x - Coordinate
        s(1,z) = s(1,z) + Cx(i+1) * Bspl;
        % y - Coordinate
        s(2,z) = s(2,z) + Cy(i+1) * Bspl;
    end
end

end

And this my "main" script:

%% Clear console
close all;
clear all;
clc;

%% Parameters
disp('>> Parameters ');

% Control points
Cx = [0 1 4 5.5 6.5 8];
Cy = [0 1 1 0.5 0.5 0];

% Degree of polynom 
m = 3;

% Calculate amount of control points 
% Control points: n + 1
n = size(Cx,2) - 1;

% Plot intervall
t = 0:0.01:n-m+1;


%% Calculate knot vector
disp('>> Knot vector');

% Knot vector T
T = [];
for j=0:1:n+m+1
    if j <= m
        a = 0;
    elseif j >= m+1 && j <= n
        a = j - m;
    elseif j > n
        a = n - m + 1;
    end
    T(j+1) = a;
end

% Knot vector output
T

%% Calculate splines
disp('>> Calculate B-Splines');

% Spline Matrx
% s(1,:) : x values
% s(2,:) : y values
s = zeros(2, size(t,2));

% Calculate B-Spline for all t
for z=1:1:size(t,2)
    % s(1,z) = Sum { x_i * B_i,m(t) }, i = 0,1, ... ,n
    % s(2,z) = Sum { y_i * B_i,m(t) }, i = 0,1, ... ,n
    s(1,z) = 0;
    s(2,z) = 0;
    for i=0:1:n
        % Calculate B-Spline
        Bspl = f_BsplineBase(i, m, t(z), T);
        % x - Coordinate
        s(1,z) = s(1,z) + Cx(i+1) * Bspl;
        % y - Coordinate
        s(2,z) = s(2,z) + Cy(i+1) * Bspl;
    end
end

%% Plot
disp('>> Plot');

figure(1);
plot(Cx, Cy, 'o');
hold on;
plot(Cx, Cy, '--');
hold on;
plot(s(1,:), s(2,:),'linewidth',2);
legend({'Control points','Polygon', 'B-Spline'},'Location','northwest');
grid on;
grid minor;

%% End
disp(' >> Finished');

It would be great if anybody could figure out the case of the problem (these strange "spikes" produced by my algorithm).

What went wrong / what is my mistake?

PS: I know that this is not a perfect code file. I am looking forward to seperate some other functions such as the calculation of

the knot vector, because it is not neccessary to calculate it in every function call.

[Ganesh Regoti]

Can you provide the f_BsplineBase function?