bsplinebasis.m

% B = bsplinebasis(degree,knots,ts)
%
% Evaluate basis for a spline of given degree and knots, at a set of parameter
% values ts.
%
% Each column corresponds to a control point and each row corresponds to one
% parameter value such that, for a column vector of control points c, the
% spline can be evaluated as:
%
% s = B.c
%
% Matthew Chapman <contact@zmatt.net>, based on algorithm in
%    C code for An Introduction to NURBS, David F. Rogers, Section 3.5

function B = bsplinebasis(degree,knots,ts)

order = degree + 1;
nknots = length(knots);
npoints = nknots-order;
B = zeros(length(ts), npoints);

for i = 1:length(ts)
  t = ts(i);
  if t == knots(nknots)
    % special case: if t is last knot, treat it as if it were
    % in the previous span, otherwise it would not be in any
    j = find(knots~=t,1,'last');
    searcht = knots(j);
  else
    searcht = t;
  end

  % calculate 1st order basis functions
  % 1 if in knot span, 0 if not
  temp = zeros(1,nknots-1);
  for j = 1:nknots-1
    temp(j) = double(searcht >= knots(j) && searcht < knots(j+1));
  end

  for k = 2:order
    % recursively calculate next order basis functions
    % by a linear combination of temp(j) and temp(j+1)
    for j = 1:nknots-k
      d = 0;
      e = 0;
      if temp(j) ~= 0
        d = ((t-knots(j))*temp(j))/(knots(j+k-1)-knots(j));
      end
      if temp(j+1) ~= 0
        e = ((knots(j+k)-t)*temp(j+1))/(knots(j+k)-knots(j+1));
      end
      temp(j) = d+e;
    end
  end

  B(i,:) = temp(1:npoints);
end

end