Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / nurbs-1.3.6 / nrbbasisfunder.m

diff --git a/octave_packages/nurbs-1.3.6/nrbbasisfunder.m b/octave_packages/nurbs-1.3.6/nrbbasisfunder.m
new file mode 100644 (file)
index 0000000..737f534
--- /dev/null
+++ b/octave_packages/nurbs-1.3.6/nrbbasisfunder.m
@@ -0,0 +1,123 @@
+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 (p, srf)
+%
+%    INPUT:
+%   
+%      u or p(1,:,:)  - parametric points along u direction
+%      v or p(2,:,:)  - parametric points along v direction
+%      crv - NURBS curve
+%      srf - NURBS surface
+%   
+%    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 2 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)
+