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nrbcoons.m
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function srf = nrbcoons(u1, u2, v1, v2)
%
% Function Name:
%
% 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= [ 0.0 3.0 5.0 8.0 10.0;
% 10.0 10.0 10.0 10.0 10.0;
% 3.0 5.0 8.0 6.0 10.0];
% crv2 = nrbmak(pnts, [0 0 0 1/3 2/3 1 1 1]);
%
% pnts= [ 0.0 0.0 0.0 0.0;
% 0.0 3.0 8.0 10.0;
% 2.0 0.0 5.0 3.0];
% crv3 = nrbmak(pnts, [0 0 0 0.5 1 1 1]);
%
% pnts= [ 10.0 10.0 10.0 10.0 10.0;
% 0.0 3.0 5.0 8.0 10.0;
% 9.0 7.0 7.0 10.0 10.0];
% 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 = [kua k(i)*ones(1,m-i1)];
kub = [kub k(i)*ones(1,m-i2)];
kuc = [kuc k(i)*ones(1,m-i3)];
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 = [kva k(i)*ones(1,m-i1)];
kvb = [kvb k(i)*ones(1,m-i2)];
kvc = [kvc k(i)*ones(1,m-i3)];
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);