/usr/share/octave/packages/nurbs-1.3.13/nrbnumbasisfun.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 | function idx = nrbnumbasisfun (points, nrb)
%
% NRBNUMBASISFUN: Numbering of basis functions for NURBS
%
% Calling Sequence:
%
% N = nrbnumbasisfun (u, crv)
% N = nrbnumbasisfun ({u, v}, srf)
% N = nrbnumbasisfun (p, srf)
% N = nrbnumbasisfun ({u, v, w}, vol)
% N = nrbnumbasisfun (p, vol)
%
% INPUT:
%
% u or p(1,:,:) - parametric points along u direction
% v or p(2,:,:) - parametric points along v direction
% w or p(3,:,:) - parametric points along w direction
% crv - NURBS curve
% srf - NURBS surface
% vol - NURBS volume
%
% OUTPUT:
%
% N - Indices of the basis functions that are nonvanishing at each
% point. size(N) == [npts, prod(nrb.order)]
%
% Copyright (C) 2009 Carlo de Falco
% Copyright (C) 2016 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 ( (nargin<2) ...
|| (nargout>1) ...
|| (~isstruct(nrb)) ...
|| (iscell(points) && ~iscell(nrb.knots)) ...
|| (~iscell(points) && iscell(nrb.knots) && (size(points,1)~=numel(nrb.number))) ...
)
error('Incorrect input arguments in nrbnumbasisfun');
end
if (~iscell(nrb.knots)) %% NURBS curve
iv = findspan (nrb.number-1, nrb.order-1, points, nrb.knots);
idx = numbasisfun (iv, points, nrb.order-1, nrb.knots);
else
ndim = numel (nrb.number);
if (iscell (points))
for idim = 1:ndim
pts_dim = points{idim};
sp{idim} = findspan (nrb.number(idim)-1, nrb.order(idim)-1, pts_dim, nrb.knots{idim});
% N{idim} = basisfun(sp{idim}, pts_dim, nrb.order(idim)-1, nrb.knots{idim});
num{idim} = numbasisfun (sp{idim}, pts_dim, nrb.order(idim)-1, nrb.knots{idim}) + 1;
end
npts_dim = cellfun (@numel, points);
cumnpts = cumprod([1 npts_dim]);
npts = prod (npts_dim);
numaux = 1;
cumorder = cumprod ([1 nrb.order]);
cumnumber = cumprod ([1 nrb.number]);
for idim = 1:ndim
num_dim = reshape (num{idim}, 1, npts_dim(idim), 1, nrb.order(idim));
num_dim = repmat (num_dim, cumnpts(idim), 1, cumorder(idim), 1);
num_prev = reshape (numaux, cumnpts(idim), 1, cumorder(idim), 1);
num_prev = repmat (num_prev, 1, npts_dim(idim), 1, nrb.order(idim));
numaux = sub2ind ([cumnumber(idim) nrb.number(idim)], num_prev, num_dim);
numaux = reshape (numaux, cumnpts(idim+1), cumorder(idim+1));
end
idx = reshape (numaux, npts, prod (nrb.order));
else
for idim = 1:ndim
pts_dim = points(idim,:);
sp{idim} = findspan (nrb.number(idim)-1, nrb.order(idim)-1, pts_dim, nrb.knots{idim});
% N{idim} = basisfun(sp{idim}, pts_dim, nrb.order(idim)-1, nrb.knots{idim});
num{idim} = numbasisfun (sp{idim}, pts_dim, nrb.order(idim)-1, nrb.knots{idim}) + 1;
end
npts = numel (points(1,:));
idx = zeros (npts, prod(nrb.order));
local_num = cell (ndim, 1);
for ipt = 1:npts
for idim = 1:ndim
local_num{idim} = num{idim}(ipt,:);
end
[local_num{:}] = ndgrid (local_num{:});
idx(ipt,:) = reshape (sub2ind (nrb.number, local_num{:}), 1, size(idx, 2));
end
end
end
end
%!test
%! p = 2; q = 3; m = 4; n = 5;
%! Lx = 1; Ly = 1;
%! nrb = nrb4surf ([0 0], [1 0], [0 1], [1 1]);
%! nrb = nrbdegelev (nrb, [p-1, q-1]);
%! ikx = linspace(0,1,m); iky = linspace(0,1,n);
%! nrb = nrbkntins (nrb, {ikx(2:end-1), iky(2:end-1)});
%! nrb.coefs (4,:,:) = nrb.coefs (4,:,:) + rand (size (nrb.coefs (4,:,:)));
%! u = rand (1, 30); v = rand (1, 10);
%! u = (u-min (u))/max (u-min (u));
%! v = (v-min (v))/max (v-min (v));
%! N = nrbnumbasisfun ({u, v}, nrb);
%! assert (all (all (N>0)), true)
%! assert (all (all (N <= prod (nrb.number))), true)
%! assert (max (max (N)), prod (nrb.number))
%! assert (min (min (N)), 1)
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