nrbeval.m

非均匀有理B样条的matlab程序

function [p,w] = nrbeval(nurbs,tt)
% 
% Function Name:
% 
%   nrbeval - Evaluate a NURBS at parameteric points
% 
% Calling Sequence:
% 
%   [p,w] = nrbeval(crv,ut)
%   [p,w] = nrbeval(srf,{ut,vt})
% 
% Parameters:
% 
%   crv		: NURBS curve, see nrbmak.
% 
%   srf		: NURBS surface, see nrbmak.
% 
%   ut		: Parametric evaluation points along U direction.
%
%   vt		: Parametric evaluation points along V direction.
% 
%   p		: Evaluated points on the NURBS curve or surface as cartesian
% 		coordinates (x,y,z). If w is included on the lhs argument list
% 		the points are returned as homogeneous coordinates (wx,wy,wz).
% 
%   w		: Weights of the homogeneous coordinates of the evaluated
% 		points. Note inclusion of this argument changes the type 
% 		of coordinates returned in p (see above).
% 
% Description:
% 
%   Evaluation of NURBS curves or surfaces at parametric points along the 
%   U and V directions. Either homogeneous coordinates are returned if the 
%   weights are requested in the lhs arguments, or as cartesian coordinates.
%   This function utilises the 'C' interface bspeval.
% 
% Examples:
% 
%   Evaluate the NURBS circle at twenty points from 0.0 to 1.0
% 
%   nrb = nrbcirc;
%   ut = linspace(0.0,1.0,20);
%   p = nrbeval(nrb,ut);
% 
% See:
%  
%     bspeval
%

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

if nargin < 2
  error('Not enough input arguments');
end

foption = 1;    % output format 3D cartesian coordinates
if nargout == 2
  foption = 0;  % output format 4D homogenous coordinates 
end
   
if ~isstruct(nurbs)
  error('NURBS representation is not structure!');
end

if ~strcmp(nurbs.form,'B-NURBS')
  error('Not a recognised NURBS representation');
end

if iscell(nurbs.knots)
  % NURBS structure represents a surface

  num1 = nurbs.number(1);
  num2 = nurbs.number(2);
  degree = nurbs.order-1;

  if iscell(tt)
    % Evaluate over a [u,v] grid
    % tt{1} represents the u direction
    % tt{2} represents the v direction

    nt1 = length(tt{1});
    nt2 = length(tt{2});
    
    % Evaluate along the v direction
    val = reshape(nurbs.coefs,4*num1,num2);
    val = bspeval(degree(2),val,nurbs.knots{2},tt{2});
    val = reshape(val,[4 num1 nt2]);
    
    % Evaluate along the u direction
    val = permute(val,[1 3 2]);
    val = reshape(val,4*nt2,num1);
    val = bspeval(degree(1),val,nurbs.knots{1},tt{1});
    val = reshape(val,[4 nt2 nt1]);
    val = permute(val,[1 3 2]);

    w = val(4,:,:);
    p = val(1:3,:,:);
    if foption
      p = p./repmat(w,[3 1 1]);
    end

  else

    % Evaluate at scattered points
    % tt(1,:) represents the u direction
    % tt(2,:) represents the v direction

    nt = size(tt,2);

    val = reshape(nurbs.coefs,4*num1,num2);
    val = bspeval(degree(2),val,nurbs.knots{2},tt(2,:));
    val = reshape(val,[4 num1 nt]);


    % evaluate along the u direction
    pnts = zeros(4,nt);
    for v = 1:nt
      coefs = squeeze(val(:,:,v));
      pnts(:,v) = bspeval(degree(1),coefs,nurbs.knots{1},tt(1,v));
    end

    w = pnts(4,:);
    p = pnts(1:3,:);
    if foption
       p = p./w;
    end
        
  end

else

  % NURBS structure represents a curve
  %  tt represent a vector of parametric points in the u direction

  val = bspeval(nurbs.order-1,nurbs.coefs,nurbs.knots,tt);   

  w = val(4,:);
  p = val(1:3,:);
  if foption
    p = p./repmat(w,3,1);
  end

end