/usr/share/octave/packages/nurbs-1.3.13/nrbunclamp.m is in octave-nurbs 1.3.13-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 | function ucrv = nrbunclamp (crv, k, xdim)
% NRBUNCLAMP: Compute the knot vector and control points of the unclamped curve or surface.
%
% Calling Sequence:
%
% ucrv = nrbrunclamp (crv, k)
% ucrv = nrbrunclamp (crv, k, dim)
%
% INPUT:
%
% crv : NURBS curve or surface, see nrbmak.
% k : continuity for the unclamping (from 0 up to p-1)
% dim : dimension in which to unclamp (all by default).
%
% OUTPUT:
%
% ucrv: NURBS curve with unclamped knot vector, see nrbmak
%
% Description:
%
% Unclamps a curve, removing the open knot vector. Computes the new
% knot vector and control points of the unclamped curve.
%
% Adapted from Algorithm A12.1 from 'The NURBS BOOK' pg577.
%
% Copyright (C) 2013, 2014 Rafael Vazquez
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
if (iscell (crv.knots))
knt = crv.knots;
curve = false;
else
knt = {crv.knots};
curve = true;
end
ndim = numel (knt);
if (nargin < 3)
xdim = 1:ndim;
end
%if (iscell (crv.knots))
if (numel(k) ~= ndim)
k = k * ones(1, ndim);
end
Pw = crv.coefs;
for idim = xdim
p = crv.order(idim) - 1;
U = knt{idim};
n = crv.number(idim);
m = n + p + 1;
kk = k(idim);
if (kk >= p)
warning ('Taking the maximum k allowed, degree - 1')
kk = p - 1;
end
% Unclamp at left end
for ii=0:kk
U(kk-ii+1) = U(kk-ii+2) - (U(n+1-ii) - U(n-ii));
end
Pw = permute (Pw, [1, circshift([2 3 4], [0, 1-idim])]);
for ii = p-kk-1:p-2
for jj = ii:-1:0
alpha = (U(p+1) - U(p+jj-ii)) / (U(p+jj+2) - U(p+jj-ii));
Pw(:,jj+1,:,:) = (Pw(:,jj+1,:,:) - alpha*Pw(:,jj+2,:,:))/(1-alpha);
end
end
% Unclamp at right end
for ii=0:kk
U(m-kk+ii) = U(m-kk+ii-1) + U(p+ii+1+1) - U(p+ii+1);
end
for ii = p-kk-1:p-2
for jj = ii:-1:0
alpha = (U(n+1)-U(n-jj))/(U(n+2-jj+ii)-U(n-jj));
Pw(:,n-jj,:,:) = (Pw(:,n-jj,:,:) - (1-alpha)*Pw(:,n-jj-1,:,:))/alpha;
end
end
Pw = permute (Pw, [1, circshift([2 3 4], [0, idim-1])]);
knt{idim} = U;
end
if (~curve)
ucrv = nrbmak (Pw, knt);
else
ucrv = nrbmak (Pw, knt{:});
end
%!demo
%! crv = nrbcirc (1,[],0,2*pi/3);
%! crv = nrbdegelev (crv, 2);
%! figure
%! nrbctrlplot (crv); hold on
%! nrbctrlplot (nrbtform (nrbunclamp (crv, 1), vectrans([-0.4, -0.4])));
%! nrbctrlplot (nrbtform (nrbunclamp (crv, 2), vectrans([-0.8, -0.8])));
%! nrbctrlplot (nrbtform (nrbunclamp (crv, 3), vectrans([-1.6, -1.6])));
%! title ('Original curve and unclamped versions')
%!test
%! crv = nrbdegelev (nrbtestcrv,2);
%! x = linspace (0, 1, 100);
%! F = nrbeval (crv, x);
%! ucrv = nrbunclamp (crv, 0);
%! assert (F, nrbeval(ucrv, x));
%! ucrv = nrbunclamp (crv, 1);
%! assert (F, nrbeval(ucrv, x), 1e-14);
%! ucrv = nrbunclamp (crv, 2);
%! assert (F, nrbeval(ucrv, x), 1e-14);
%! ucrv = nrbunclamp (crv, 3);
%! assert (F, nrbeval(ucrv, x), 1e-14);
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