nrbmak.m

强大的nurbs的工具箱 nurbs曲线

function nurbs = nrbmak(coefs,knots)
%
% Function Name:
% 
%   nrbmak - Construct the NURBS structure given the control points
%            and the knots.
% 
% Calling Sequence:
% 
%   nurbs   = nrbmak(cntrl,knots);
% 
% Parameters:
% 
%   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) and for a surface a multidimensional
% 		array of size (dim,nu,nv). Where nu is number of points along
% 		the parametric U direction, and nv the number of points
%               along the V 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 curves and surfaces
%               are clamped to the start and end control points by knot
%               multiplicities equal to the spline order.
%               For curve knots form a vector and for a surface the knot
%               are stored by two vectors for U and V in a cell structure.
%               {uknots vknots}
%               
%   nurbs 	: Data structure for representing a NURBS curve.
% 
% 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 degree is a vector [du,dv] containing the degree
%   along the U and V directions respectively.
% 
% 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]);

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

nurbs.form   = 'B-NURBS';
nurbs.dim    = 4;
np = size(coefs);
dim = np(1);
if iscell(knots)
  % 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];

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