Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / nurbs-1.3.6 / nrbcirc.m

diff --git a/octave_packages/nurbs-1.3.6/nrbcirc.m b/octave_packages/nurbs-1.3.6/nrbcirc.m
new file mode 100644 (file)
index 0000000..435ef91
--- /dev/null
+++ b/octave_packages/nurbs-1.3.6/nrbcirc.m
@@ -0,0 +1,123 @@
+function curve = nrbcirc(radius,center,sang,eang)
+% 
+% NRBCIRC: Construct a circular arc.
+% 
+% Calling Sequence:
+% 
+%   crv = nrbcirc()
+%   crv = nrbcirc(radius)
+%   crv = nrbcirc(radius,center)
+%   crv = nrbcirc(radius,center,sang,eang)
+% 
+% INPUT:
+% 
+%   radius     : Radius of the circle, default 1.0
+% 
+%   center     : Center of the circle, default (0,0,0)
+% 
+%   sang       : Start angle, default 0 radians (0 degrees)
+% 
+%   eang       : End angle, default 2*pi radians (360 degrees)
+% 
+% OUTPUT:
+%
+%   crv                : NURBS curve for a circular arc.
+% 
+% Description:
+% 
+%   Constructs NURBS data structure for a circular arc in the x-y plane. If
+%   no rhs arguments are supplied a unit circle with center (0.0,0.0) is
+%   constructed. 
+% 
+%   Angles are defined as positive in the anti-clockwise direction.
+%
+%    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 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/>.
+
+if nargin < 1
+  radius = 1;
+end
+
+if nargin < 2
+  center = [];
+end
+   
+if nargin < 4
+  sang = 0;
+  eang = 2*pi;
+end
+
+sweep = eang - sang;       % sweep angle of arc
+if sweep < 0
+  sweep = 2*pi + sweep;
+end
+     
+if abs(sweep) <= pi/2
+  narcs = 1;                % number of arc segments
+  knots = [0 0 0 1 1 1];
+elseif abs(sweep) <= pi
+  narcs = 2;
+  knots = [0 0 0 0.5 0.5 1 1 1];
+elseif abs(sweep) <= 3*pi/2
+  narcs = 3;
+  knots = [0 0 0 1/3 1/3 2/3 2/3 1 1 1];
+else
+  narcs = 4;
+  knots = [0 0 0 0.25 0.25 0.5 0.5 0.75 0.75 1 1 1];
+end
+
+dsweep = sweep/(2*narcs);     % arc segment sweep angle/2
+
+% determine middle control point and weight
+wm = cos(dsweep);
+x  = radius*wm;
+y  = radius*sin(dsweep);
+xm = x+y*tan(dsweep);
+
+% arc segment control points
+ctrlpt = [ x wm*xm x;    % w*x - coordinate
+          -y 0     y;    % w*y - coordinate
+           0 0     0;    % w*z - coordinate
+           1 wm    1];   % w   - coordinate
+      
+% build up complete arc from rotated segments
+coefs = zeros(4,2*narcs+1);   % nurbs control points of arc
+xx = vecrotz(sang + dsweep);
+coefs(:,1:3) = xx*ctrlpt;     % rotate to start angle
+xx = vecrotz(2*dsweep);
+for n = 2:narcs
+   m = 2*n+[0 1];
+   coefs(:,m) = xx*coefs(:,m-2);
+end
+
+% vectrans arc if necessary
+if ~isempty(center) 
+  xx = vectrans(center);
+  coefs = xx*coefs;
+end
+
+curve = nrbmak(coefs,knots);
+
+end
+
+%!demo
+%! for r = 1:9
+%! crv = nrbcirc(r,[],deg2rad(45),deg2rad(315));
+%!   nrbplot(crv,50);
+%!   hold on;
+%! end
+%! hold off;
+%! axis equal;
+%! title('NURBS construction of several 2D arcs.');