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Sourcecode: octave-nurbs version File versions  Download package

nrbcirc.m

function curve = nrbcirc(radius,center,sang,eang)
% 
% NRBCIRC: Construct a circular arc.
% 
% Calling Sequence:
% 
%   crv = nrbarc()
%   crv = nrbarc(radius)
%   crv = nrbarc(radius,center)
%   crv = nrbarc(radius,center,sang,eang)
% 
% Parameters:
% 
%   radius  : Radius of the circle, default 1.0
% 
%   center  : Center of the circle, default (0,0,0)
% 
%   sang    : Start angle, default 0 degrees
% 
%   eang    : End angle 360 degrees
% 
%   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.

%  D.M. Spink
%  Copyright (c) 2000.

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);

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