/usr/share/octave/packages/nurbs-1.3.7/nrbmak.m is in octave-nurbs 1.3.7-1build1.
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%
% 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.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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