Add a useful package (from Source forge) for octave

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

diff --git a/octave_packages/nurbs-1.3.6/nrbbasisfun.m b/octave_packages/nurbs-1.3.6/nrbbasisfun.m
new file mode 100644 (file)
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+++ b/octave_packages/nurbs-1.3.6/nrbbasisfun.m
@@ -0,0 +1,137 @@
+function [B, id] = nrbbasisfun (points, nrb)
+
+% NRBBASISFUN: Basis functions for NURBS
+%
+% Calling Sequence:
+% 
+%    B     = nrbbasisfun (u, crv)
+%    B     = nrbbasisfun ({u, v}, srf)
+%   [B, N] = nrbbasisfun ({u, v}, srf)
+%   [B, N] = nrbbasisfun (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:
+%   
+%      B - Value of the basis functions at the points
+%          size(B)=[numel(u),(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>2) ...
+      || (~isstruct(nrb)) ...
+      || (iscell(points) && ~iscell(nrb.knots)) ...
+      || (~iscell(points) && iscell(nrb.knots) && (size(points,1)~=2)) ...
+      || (~iscell(nrb.knots) && (nargout>1)) ...
+      )
+    error('Incorrect input arguments in nrbbasisfun');
+  end
+                            
+  if (~iscell(nrb.knots))         %% NURBS curve
+    
+    [B, id] = nrb_crv_basisfun__ (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
+    
+    [B, id] = nrb_srf_basisfun__ (p, nrb); 
+
+  else                            %% NURBS volume
+    error('The function nrbbasisfun 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);
+%! B = nrbbasisfun (u, nrb);
+%! xplot = sum(bsxfun(@(x,y) x.*y, B, x),2);
+%! plot(xplot, B)
+%! title('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);
+%! B = nrbbasisfun (u, nrb);
+%! xplot = sum(bsxfun(@(x,y) x.*y, B, x),2);
+%!
+%! yy = y; yy(1) = 1;
+%! nrb2 = nrbmak ([x.*w;yy;y;w], U); 
+%! aux = nrbeval(nrb2,u);
+%! %figure, plot(xplot, B(:,1), aux(1,:).', w(1)*aux(2,:).')
+%! assert(B(:,1), w(1)*aux(2,:).', 1e-6)
+%! 
+%! yy = y; yy(2) = 1;
+%! nrb2 = nrbmak ([x.*w;yy;y;w], U);
+%! aux = nrbeval(nrb2, u);
+%! %figure, plot(xplot, B(:,2), aux(1,:).', w(2)*aux(2,:).')
+%! assert(B(:,2), w(2)*aux(2,:).', 1e-6)
+%!
+%! yy = y; yy(3) = 1;
+%! nrb2 = nrbmak ([x.*w;yy;y;w], U);
+%! aux = nrbeval(nrb2,u);
+%! %figure, plot(xplot, B(:,3), aux(1,:).', w(3)*aux(2,:).')
+%! assert(B(:,3), w(3)*aux(2,:).', 1e-6)
+%!
+%! yy = y; yy(4) = 1;
+%! nrb2 = nrbmak ([x.*w;yy;y;w], U);
+%! aux = nrbeval(nrb2,u);
+%! %figure, plot(xplot, B(:,4), aux(1,:).', w(4)*aux(2,:).')
+%! assert(B(:,4), w(4)*aux(2,:).', 1e-6)
+
+%!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)});
+%! u = rand (1, 30); v = rand (1, 10);
+%! u = u - min (u); u = u / max (u);
+%! v = v - min (v); v = v / max (v);
+%! [B, N] = nrbbasisfun ({u, v}, nrb);
+%! assert (sum(B, 2), ones(300, 1), 1e-6)
+%! assert (all (all (B<=1)), true)
+%! assert (all (all (B>=0)), true)
+%! 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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