octave-nurbs 1.3.10-1 / usr / share / octave / packages / nurbs-1.3.10 / nrbmak.m

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 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/>.

nurbs = struct ('form', 'B-NURBS', 'dim', 4, 'number', [], 'coefs', [], ...
                'knots', [], 'order', []);

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(uorder))/(uknots(end-uorder+1)-uknots(uorder));
%   vknots = (vknots-vknots(vorder))/(vknots(end-vorder+1)-vknots(vorder));
%   wknots = (wknots-wknots(worder))/(wknots(end-worder+1)-wknots(worder));
   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(uorder))/(uknots(end-uorder+1)-uknots(uorder));
%   vknots = (vknots-vknots(vorder))/(vknots(end-vorder+1)-vknots(vorder));
   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
  order = size (knots,2) - np(2);
  nurbs.order = order;
  knots = sort(knots);
%  nurbs.knots = (knots-knots(order))/(knots(end-order+1)-knots(order));
  nurbs.knots = knots;

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