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nrbcoons.m

function srf = nrbcoons(u1, u2, v1, v2)
% 
% NRBCOONS: Construction of a Coons patch.
% 
% Calling Sequence:
% 
%   srf = nrbcoons(ucrv1, ucrv2, vcrv1, vcrv2)
% 
% Parameters:
% 
%  ucrv1    : NURBS curve defining the bottom U direction boundary of
%           the constructed NURBS surface.
% 
%   ucrv2   : NURBS curve defining the top U direction boundary of
%           the constructed NURBS surface.
% 
%   vcrv1   : NURBS curve defining the bottom V direction boundary of
%           the constructed NURBS surface.
% 
%   vcrv2   : NURBS curve defining the top V direction boundary of
%           the constructed NURBS surface.
% 
%   srf           : Coons NURBS surface patch.
% 
% Description:
% 
%   Construction of a bilinearly blended Coons surface patch from four NURBS
%   curves that define the boundary.
% 
%   The orientation of the four NURBS boundary curves.
% 
%          ^ V direction
%          |
%          |     ucrv2
%          ------->--------
%          |              |
%          |              |
%    vcrv1 ^   Surface    ^ vcrv2
%          |              |
%          |              |
%          ------->-----------> U direction
%                ucrv1
% 
% 
% Examples:
% 
%   // Define four NURBS curves and construct a Coons surface patch.
%   pnts = [ 0.0  3.0  4.5  6.5 8.0 10.0;
%            0.0  0.0  0.0  0.0 0.0  0.0; 
%            2.0  2.0  7.0  4.0 7.0  9.0];   
%   crv1 = nrbmak(pnts, [0 0 0 1/3 0.5 2/3 1 1 1]);
% 
%   pnts= ;
%   crv2 = nrbmak(pnts, [0 0 0 1/3 2/3 1 1 1]);
% 
%   pnts= ;
%   crv3 = nrbmak(pnts, [0 0 0 0.5 1 1 1]);
% 
%   pnts= ;
%   crv4 = nrbmak(pnts, [0 0 0 0.25 0.75 1 1 1]);
% 
%   srf = nrbcoons(crv1, crv2, crv3, crv4);
%   nrbplot(srf,[20 20],220,45);

%  D.M. Spink
%  Copyright (c) 2000.

if nargin ~= 4
  error('Incorrect number of input arguments');
end

r1 = nrbruled(u1, u2);
r2 = nrbtransp(nrbruled(v1, v2));
t  = nrb4surf(u1.coefs(:,1), u1.coefs(:,end), u2.coefs(:,1), u2.coefs(:,end));

% raise all surfaces to a common degree
du = max([r1.order(1), r2.order(1), t.order(1)]);
dv = max([r1.order(2), r2.order(2), t.order(2)]);
r1 = nrbdegelev(r1, [du - r1.order(1), dv - r1.order(2)]);
r2 = nrbdegelev(r2, [du - r2.order(1), dv - r2.order(2)]);
t  = nrbdegelev(t,  [du - t.order(1),  dv - t.order(2)]);

% merge the knot vectors, to obtain a common knot vector

% U knots
k1 = r1.knots{1};
k2 = r2.knots{1};
k3 = t.knots{1};
k = unique([k1 k2 k3]);
n = length(k);
kua = ;
kub = ;
kuc = ;
for i = 1:n
  i1 = length(find(k1 == k(i)));
  i2 = length(find(k2 == k(i)));
  i3 = length(find(k3 == k(i)));
  m = max([i1, i2, i3]);
  kua = ;  
  kub = ;
  kuc = ;
end  

% V knots
k1 = r1.knots{2};
k2 = r2.knots{2};
k3 = t.knots{2};
k = unique([k1 k2 k3]);
n = length(k);
kva = ;
kvb = ;
kvc = ;
for i = 1:n
  i1 = length(find(k1 == k(i)));
  i2 = length(find(k2 == k(i)));
  i3 = length(find(k3 == k(i)));
  m = max([i1, i2, i3]);
  kva = ;  
  kvb = ;
  kvc = ;
end  

r1 = nrbkntins(r1, {kua, kva});
r2 = nrbkntins(r2, {kub, kvb});
t  = nrbkntins(t,  {kuc, kvc});

% combine coefficient to construct Coons surface
coefs(1,:,:) = r1.coefs(1,:,:) + r2.coefs(1,:,:) - t.coefs(1,:,:);
coefs(2,:,:) = r1.coefs(2,:,:) + r2.coefs(2,:,:) - t.coefs(2,:,:);
coefs(3,:,:) = r1.coefs(3,:,:) + r2.coefs(3,:,:) - t.coefs(3,:,:);
coefs(4,:,:) = r1.coefs(4,:,:) + r2.coefs(4,:,:) - t.coefs(4,:,:);
srf = nrbmak(coefs, r1.knots);


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