3D Rational Bezier Curve (Matlab Code)

 

% % % --------------------------------
% % % Author: begtostudy
% % % Email : begtostudy@gmail.com
% % % --------------------------------
function Q=bezier(P,t,w)
% Rational Bezier interpolation for given points.
%
%Example:
% P=[1 0 0 ;1 0.5 0; 0 0 -1;0 1 1;0 1 0]';
% w=[12, 6,1,-3,12];
% 
% t=linspace(0,1,100);
% [Q3D]=bezier(P,t,w);//curve on sphere
% 
% figure
% plot3(Q3D(1,:),Q3D(2,:),Q3D(3,:),'b','LineWidth',2),
% hold on
% plot3(P(1,:),P(2,:),P(3,:),'g:','LineWidth',2)        % plot control polygon
% plot3(P(1,:),P(2,:),P(3,:),'ro','LineWidth',2)     % plot control points
% view(3);
% box;
if (nargin==2)
  w=ones(1,size(P,2));
end
for k=1:length(t)
    Q(:,k)=[0 0 0]';
    rational=0;
    for j=1:size(P,2)
        tmp=Bernstein(size(P,2)-1,j-1,t(k));
        if (nargin==3)
        rational=rational+w(j)*tmp;
        end
        Q(:,k)=Q(:,k)+w(j)*P(:,j)*tmp;
    end
    if (nargin==3)
    Q(:,k)=Q(:,k)./rational;
    end
end
end
 
function B=Bernstein(n,j,t)
    B=factorial(n)/(factorial(j)*factorial(n-j))*(t^j)*(1-t)^(n-j);
end