function nurbs = nrbmak(coefs,knots) % % 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

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