/usr/share/octave/packages/nurbs-1.3.13/nrbcoons.m is in octave-nurbs 1.3.13-4.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 | function srf = nrbcoons(u1, u2, v1, v2)
%
% NRBCOONS: Construction of a Coons patch.
%
% Calling Sequence:
%
% srf = nrbcoons(ucrv1, ucrv2, vcrv1, vcrv2)
%
% INPUT:
%
% 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.
%
% OUTPUT:
%
% 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);
%
% Copyright (C) 2000 Mark Spink
%
% 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 ~= 4
error('Incorrect number of input arguments');
end
if (max (abs (nrbeval (u1, u1.knots(1)) - nrbeval (v1, v1.knots(1)))) > 1e-10 || ...
max (abs (nrbeval (u1, u1.knots(end)) - nrbeval (v2, v2.knots(1)))) > 1e-10 || ...
max (abs (nrbeval (u2, u2.knots(1)) - nrbeval (v1, v1.knots(end)))) > 1e-10 || ...
max (abs (nrbeval (u2, u2.knots(end)) - nrbeval (v2, v2.knots(end)))) > 1e-10)
error ('The four curves do not define a closed boundary')
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);
end
%!demo
%! 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]);
%! title('Construction of a bilinearly blended Coons surface.');
%! hold off
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