/usr/share/octave/packages/nurbs-1.3.10/nrbbasisfunder.m is in octave-nurbs 1.3.10-1.
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 | function varargout = nrbbasisfunder (points, nrb)
% NRBBASISFUNDER: NURBS basis functions derivatives
%
% Calling Sequence:
%
% Bu = nrbbasisfunder (u, crv)
% [Bu, N] = nrbbasisfunder (u, crv)
% [Bu, Bv] = nrbbasisfunder ({u, v}, srf)
% [Bu, Bv, N] = nrbbasisfunder ({u, v}, srf)
% [Bu, Bv, N] = nrbbasisfunder (pts, srf)
%
% INPUT:
%
% u - parametric coordinates along u direction
% v - parametric coordinates along v direction
% pts - array of scattered points in parametric domain, array size: (2,num_points)
% crv - NURBS curve
% srf - NURBS surface
%
% If the parametric coordinates are given in a cell-array, the values
% are computed in a tensor product set of points
%
% OUTPUT:
%
% Bu - Basis functions derivatives WRT direction u
% size(Bu)=[numel(u),(p+1)] for curves
% or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
%
% Bv - Basis functions derivatives WRT direction v
% size(Bv)=[numel(v),(p+1)] for curves
% or [numel(u)*numel(v), (p+1)*(q+1)] for surfaces
%
% N - Indices of the basis functions that are nonvanishing at each
% point. size(N) == size(B)
%
% Copyright (C) 2009 Carlo de Falco
%
% 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>3) ...
|| (~isstruct(nrb)) ...
|| (iscell(points) && ~iscell(nrb.knots)) ...
|| (~iscell(points) && iscell(nrb.knots) && (size(points,1)~=2)) ...
|| (~iscell(nrb.knots) && (nargout>2)) ...
)
error('Incorrect input arguments in nrbbasisfun');
end
if (~iscell(nrb.knots)) %% NURBS curve
[varargout{1}, varargout{2}] = nrb_crv_basisfun_der__ (points, nrb);
elseif size(nrb.knots,2) == 2 %% NURBS surface
if (iscell(points))
[v, u] = meshgrid(points{2}, points{1});
p = [u(:), v(:)]';
else
p = points;
end
[varargout{1}, varargout{2}, varargout{3}] = nrb_srf_basisfun_der__ (p, nrb);
else %% NURBS volume
error('The function nrbbasisfunder is not yet ready for volumes')
end
end
%!demo
%! U = [0 0 0 0 1 1 1 1];
%! x = [0 1/3 2/3 1] ;
%! y = [0 0 0 0];
%! w = [1 1 1 1];
%! nrb = nrbmak ([x;y;y;w], U);
%! u = linspace(0, 1, 30);
%! [Bu, id] = nrbbasisfunder (u, nrb);
%! plot(u, Bu)
%! title('Derivatives of the cubic Bernstein polynomials')
%! hold off
%!test
%! U = [0 0 0 0 1 1 1 1];
%! x = [0 1/3 2/3 1] ;
%! y = [0 0 0 0];
%! w = rand(1,4);
%! nrb = nrbmak ([x;y;y;w], U);
%! u = linspace(0, 1, 30);
%! [Bu, id] = nrbbasisfunder (u, nrb);
%! #plot(u, Bu)
%! assert (sum(Bu, 2), zeros(numel(u), 1), 1e-10),
%!test
%! U = [0 0 0 0 1/2 1 1 1 1];
%! x = [0 1/4 1/2 3/4 1] ;
%! y = [0 0 0 0 0];
%! w = rand(1,5);
%! nrb = nrbmak ([x;y;y;w], U);
%! u = linspace(0, 1, 300);
%! [Bu, id] = nrbbasisfunder (u, nrb);
%! assert (sum(Bu, 2), zeros(numel(u), 1), 1e-10)
%!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]);
%! aux1 = linspace(0,1,m); aux2 = linspace(0,1,n);
%! nrb = nrbkntins (nrb, {aux1(2:end-1), aux2(2:end-1)});
%! nrb.coefs (4,:,:) = nrb.coefs(4,:,:) + rand (size (nrb.coefs (4,:,:)));
%! [Bu, Bv, N] = nrbbasisfunder ({rand(1, 20), rand(1, 20)}, nrb);
%! #plot3(squeeze(u(1,:,:)), squeeze(u(2,:,:)), reshape(Bu(:,10), 20, 20),'o')
%! assert (sum (Bu, 2), zeros(20^2, 1), 1e-10)
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