testcrdnd.m

close all, clear all,clc
disp('N-Dimensional Cardinal (Catmull-Rom) Spline Interpolation v1.2 ')
str=sprintf('%s','Copyright M Khan: [e-mail]'); disp(str);
n=100;          % number of intervals (i.e. parametric curve would be evaluted n+1 times)


%%%% Cardinal Spline 1D Interpolation %%%%%%%%%%
x=[35 35 16 15 25 40 65 50 60 80 80];	
figure
hold on    
Tension=0; 
for k=1:length(x)-3
    xi=crdatnplusoneval([x(k)],[x(k+1)],[x(k+2)],[x(k+3)],Tension,n);
    plot(xi,'linewidth',2);        
    plot(xi(1),'ro','linewidth',2) ;
    plot(length(xi),xi(length(xi)),'ro','linewidth',2) ;
end
%%% Cardinal Spline 1D Interpolation 


%%%% Cardinal Spline 2D Interpolation %%%%%%%%%%
Px=[35 35 16 15 25 40 65 50 60 80 80];	
Py=[47 47 40 15 36 15 25 40 42 27 27];	
% Note first and last points are repeated so that spline curve passes
% through all points

% when Tension=0 the class of Cardinal spline is known as Catmull-Rom spline
Tension=0; 
figure
% plot(Px,Py,'ro','linewidth',2) 
hold on
for k=1:length(Px)-3
    
    [MatOut2]=crdatnplusoneval([Px(k),Py(k)],[Px(k+1),Py(k+1)],[Px(k+2),Py(k+2)],[Px(k+3),Py(k+3)],Tension,n);
    
    % Between each pair of control points plotting n+1 values of first two rows of MatOut 
    plot(MatOut2(1,:),MatOut2(2,:),'b','linewidth',2) 
end
title('\bf2D Cardinal Spline')
%%%% Cardinal Spline 2D Interpolation 


%%%% Cardinal Spline 3D Interpolation %%%%%%%%%%
 Px=[35  35  16 15 25 40 65 50 60 80 80];	
 Py=[47  47  40 15 36 15 25 40 42 27 27];	
 Pz=[-17 -17 20 15 36 15 25 20 25 -7 -7];	

% Note first and last points are repeated so that spline curve passes
% through all points

figure
hold on
plot3(Px,Py,Pz,'ro','linewidth',2) 
Tension=0; 
for k=1:length(Px)-3
    
    [MatOut3]=crdatnplusoneval([Px(k),Py(k),Pz(k)],[Px(k+1),Py(k+1),Pz(k+1)],[Px(k+2),Py(k+2),Pz(k+2)],[Px(k+3),Py(k+3),Pz(k+3)],Tension,n);
    
    % Between each pair of control points plotting n+1 values of first three rows of MatOut 
    plot3(MatOut3(1,:),MatOut3(2,:),MatOut3(3,:),'b','linewidth',2) 

end
title('\bf3D Cardinal Spline')
view(3);
box;
%%%% Cardinal Spline 3D Interpolation 

% Using similar approach you can do Cardinal Spline interpolation for
% N-Dimensional data


% % % --------------------------------
% % % Author: Dr. Murtaza Khan
% % % Email : [e-mail]
% % % --------------------------------