--- /dev/null
+function nurbs = nrbmak(coefs,knots)
+%
+% NRBMAK: Construct the NURBS structure given the control points
+% and the knots.
+%
+% Calling Sequence:
+%
+% nurbs = nrbmak(cntrl,knots);
+%
+% INPUT:
+%
+% cntrl : Control points, these can be either Cartesian or
+% homogeneous coordinates.
+%
+% For a curve the control points are represented by a
+% matrix of size (dim,nu), for a surface a multidimensional
+% array of size (dim,nu,nv), for a volume a multidimensional array
+% of size (dim,nu,nv,nw). Where nu is number of points along
+% the parametric U direction, nv the number of points along
+% the V direction and nw the number of points along the W direction.
+% dim is the dimension. Valid options
+% are
+% 2 .... (x,y) 2D Cartesian coordinates
+% 3 .... (x,y,z) 3D Cartesian coordinates
+% 4 .... (wx,wy,wz,w) 4D homogeneous coordinates
+%
+% knots : Non-decreasing knot sequence spanning the interval
+% [0.0,1.0]. It's assumed that the geometric entities
+% are clamped to the start and end control points by knot
+% multiplicities equal to the spline order (open knot vector).
+% For curve knots form a vector and for surfaces (volumes)
+% the knots are stored by two (three) vectors for U and V (and W)
+% in a cell structure {uknots vknots} ({uknots vknots wknots}).
+%
+% OUTPUT:
+%
+% nurbs : Data structure for representing a NURBS entity
+%
+% NURBS Structure:
+%
+% Both curves and surfaces are represented by a structure that is
+% compatible with the Spline Toolbox from Mathworks
+%
+% nurbs.form .... Type name 'B-NURBS'
+% nurbs.dim .... Dimension of the control points
+% nurbs.number .... Number of Control points
+% nurbs.coefs .... Control Points
+% nurbs.order .... Order of the spline
+% nurbs.knots .... Knot sequence
+%
+% Note: the control points are always converted and stored within the
+% NURBS structure as 4D homogeneous coordinates. A curve is always stored
+% along the U direction, and the vknots element is an empty matrix. For
+% a surface the spline order is a vector [du,dv] containing the order
+% along the U and V directions respectively. For a volume the order is
+% a vector [du dv dw]. Recall that order = degree + 1.
+%
+% Description:
+%
+% This function is used as a convenient means of constructing the NURBS
+% data structure. Many of the other functions in the toolbox rely on the
+% NURBS structure been correctly defined as shown above. The nrbmak not
+% only constructs the proper structure, but also checks for consistency.
+% The user is still free to build his own structure, in fact a few
+% functions in the toolbox do this for convenience.
+%
+% Examples:
+%
+% Construct a 2D line from (0.0,0.0) to (1.5,3.0).
+% For a straight line a spline of order 2 is required.
+% Note that the knot sequence has a multiplicity of 2 at the
+% start (0.0,0.0) and end (1.0 1.0) in order to clamp the ends.
+%
+% line = nrbmak([0.0 1.5; 0.0 3.0],[0.0 0.0 1.0 1.0]);
+% nrbplot(line, 2);
+%
+% Construct a surface in the x-y plane i.e
+%
+% ^ (0.0,1.0) ------------ (1.0,1.0)
+% | | |
+% | V | |
+% | | Surface |
+% | | |
+% | | |
+% | (0.0,0.0) ------------ (1.0,0.0)
+% |
+% |------------------------------------>
+% U
+%
+% coefs = cat(3,[0 0; 0 1],[1 1; 0 1]);
+% knots = {[0 0 1 1] [0 0 1 1]}
+% plane = nrbmak(coefs,knots);
+% nrbplot(plane, [2 2]);
+%
+% Copyright (C) 2000 Mark Spink, 2010 Rafael Vazquez
+%
+% 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/>.
+
+nurbs.form = 'B-NURBS';
+nurbs.dim = 4;
+np = size(coefs);
+dim = np(1);
+if iscell(knots)
+ if size(knots,2) == 3
+ if (numel(np) == 3)
+ np(4) = 1;
+ elseif (numel(np)==2)
+ np(3:4) = 1;
+ end
+ % constructing a volume
+ nurbs.number = np(2:4);
+ if (dim < 4)
+ nurbs.coefs = repmat([0.0 0.0 0.0 1.0]',[1 np(2:4)]);
+ nurbs.coefs(1:dim,:,:) = coefs;
+ else
+ nurbs.coefs = coefs;
+ end
+ uorder = size(knots{1},2)-np(2);
+ vorder = size(knots{2},2)-np(3);
+ worder = size(knots{3},2)-np(4);
+ uknots = sort(knots{1});
+ vknots = sort(knots{2});
+ wknots = sort(knots{3});
+ uknots = (uknots-uknots(1))/(uknots(end)-uknots(1));
+ vknots = (vknots-vknots(1))/(vknots(end)-vknots(1));
+ wknots = (wknots-wknots(1))/(wknots(end)-wknots(1));
+ nurbs.knots = {uknots vknots wknots};
+ nurbs.order = [uorder vorder worder];
+
+ elseif size(knots,2) == 2
+ if (numel(np)==2); np(3) = 1; end
+ % constructing a surface
+ nurbs.number = np(2:3);
+ if (dim < 4)
+ nurbs.coefs = repmat([0.0 0.0 0.0 1.0]',[1 np(2:3)]);
+ nurbs.coefs(1:dim,:,:) = coefs;
+ else
+ nurbs.coefs = coefs;
+ end
+ uorder = size(knots{1},2)-np(2);
+ vorder = size(knots{2},2)-np(3);
+ uknots = sort(knots{1});
+ vknots = sort(knots{2});
+ uknots = (uknots-uknots(1))/(uknots(end)-uknots(1));
+ vknots = (vknots-vknots(1))/(vknots(end)-vknots(1));
+ nurbs.knots = {uknots vknots};
+ nurbs.order = [uorder vorder];
+
+ end
+
+else
+
+ % constructing a curve
+ nurbs.number = np(2);
+ if (dim < 4)
+ nurbs.coefs = repmat([0.0 0.0 0.0 1.0]',[1 np(2)]);
+ nurbs.coefs(1:dim,:) = coefs;
+ else
+ nurbs.coefs = coefs;
+ end
+ nurbs.order = size(knots,2)-np(2);
+ knots = sort(knots);
+ nurbs.knots = (knots-knots(1))/(knots(end)-knots(1));
+
+end
+
+end
+
+%!demo
+%! pnts = [0.5 1.5 4.5 3.0 7.5 6.0 8.5;
+%! 3.0 5.5 5.5 1.5 1.5 4.0 4.5;
+%! 0.0 0.0 0.0 0.0 0.0 0.0 0.0];
+%! crv = nrbmak(pnts,[0 0 0 1/4 1/2 3/4 3/4 1 1 1]);
+%! nrbplot(crv,100)
+%! title('Test curve')
+%! hold off
+
+%!demo
+%! pnts = [0.5 1.5 4.5 3.0 7.5 6.0 8.5;
+%! 3.0 5.5 5.5 1.5 1.5 4.0 4.5;
+%! 0.0 0.0 0.0 0.0 0.0 0.0 0.0];
+%! crv = nrbmak(pnts,[0 0 0 0.1 1/2 3/4 3/4 1 1 1]);
+%! nrbplot(crv,100)
+%! title('Test curve with a slight variation of the knot vector')
+%! hold off
+
+%!demo
+%! pnts = zeros(3,5,5);
+%! pnts(:,:,1) = [ 0.0 3.0 5.0 8.0 10.0;
+%! 0.0 0.0 0.0 0.0 0.0;
+%! 2.0 2.0 7.0 7.0 8.0];
+%! pnts(:,:,2) = [ 0.0 3.0 5.0 8.0 10.0;
+%! 3.0 3.0 3.0 3.0 3.0;
+%! 0.0 0.0 5.0 5.0 7.0];
+%! pnts(:,:,3) = [ 0.0 3.0 5.0 8.0 10.0;
+%! 5.0 5.0 5.0 5.0 5.0;
+%! 0.0 0.0 5.0 5.0 7.0];
+%! pnts(:,:,4) = [ 0.0 3.0 5.0 8.0 10.0;
+%! 8.0 8.0 8.0 8.0 8.0;
+%! 5.0 5.0 8.0 8.0 10.0];
+%! pnts(:,:,5) = [ 0.0 3.0 5.0 8.0 10.0;
+%! 10.0 10.0 10.0 10.0 10.0;
+%! 5.0 5.0 8.0 8.0 10.0];
+%!
+%! knots{1} = [0 0 0 1/3 2/3 1 1 1];
+%! knots{2} = [0 0 0 1/3 2/3 1 1 1];
+%!
+%! srf = nrbmak(pnts,knots);
+%! nrbplot(srf,[20 20])
+%! title('Test surface')
+%! hold off
+
+%!demo
+%! coefs =[ 6.0 0.0 6.0 1;
+%! -5.5 0.5 5.5 1;
+%! -5.0 1.0 -5.0 1;
+%! 4.5 1.5 -4.5 1;
+%! 4.0 2.0 4.0 1;
+%! -3.5 2.5 3.5 1;
+%! -3.0 3.0 -3.0 1;
+%! 2.5 3.5 -2.5 1;
+%! 2.0 4.0 2.0 1;
+%! -1.5 4.5 1.5 1;
+%! -1.0 5.0 -1.0 1;
+%! 0.5 5.5 -0.5 1;
+%! 0.0 6.0 0.0 1]';
+%! knots = [0 0 0 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 1 1 1];
+%!
+%! crv = nrbmak(coefs,knots);
+%! nrbplot(crv,100);
+%! grid on;
+%! title('3D helical curve.');
+%! hold off
+
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