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1 function [rs,thetas,zs] = EDB1coordtrans1(xsou,xwedge,nvec1)
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2 % EDB1coordtrans1 - Transforms one set of cartesian coordinates to edge-related cylindrical coordinates.
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3 % The cyl. coord. system is defined so that:
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4 % A z-axis is placed along the edge, from the given endpoint 1 to the given
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5 % endpoint 2.
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6 % The origo of the cyl. syst. will be edge endpoint 1.
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7 % The theta-angles of the cyl. coord. syst. will refer to the
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8 % reference plane of the edge.
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9 % The ref. plane of the edge is described by its normal vector.
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10 % NB! The order of the edge points is important!!
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11 % The vector going from xwedge(1,:) to xwedge(2,:) must be
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12 % oriented so that if the RH thumb is along this vector, the tips
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13 % of the fingers "come out of" the open face of plane1, i.e. where nvec1
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14 % is the normal vector.
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15 %
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16 % Input parameters:
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17 % xsou Matrix, [n1,3] of cartesian coordinates of n1 points.
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18 % xwedge Matrix, [2,3], with the cartesian coordinates of the two
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19 % wedge end points: [xw1 yw1 zw1;xw2 yw2 zw2].
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20 % nvec1 List, [1,3], with the normal vector of the reference plane
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21 % of the edge.
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22 %
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23 % Output parameters:
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24 % rs, thetas, zs cyl. coord. of the points in xsou
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25 %
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26 % Uses the function EDB1cross
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27 %
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28 % ----------------------------------------------------------------------------------------------
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29 % This file is part of the Edge Diffraction Toolbox by Peter Svensson.
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30 %
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31 % The Edge Diffraction Toolbox is free software: you can redistribute it and/or modify
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32 % it under the terms of the GNU General Public License as published by the Free Software
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33 % Foundation, either version 3 of the License, or (at your option) any later version.
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34 %
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35 % The Edge Diffraction Toolbox is distributed in the hope that it will be useful,
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36 % but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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37 % FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
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38 %
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39 % You should have received a copy of the GNU General Public License along with the
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40 % Edge Diffraction Toolbox. If not, see <http://www.gnu.org/licenses/>.
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41 % ----------------------------------------------------------------------------------------------
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42 % Peter Svensson (svensson@iet.ntnu.no) 20061118
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43 %
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44 % [rs,thetas,zs] = EDB1coordtrans1(xsou,xwedge,nvec1)
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45
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46 npoints = size(xsou,1);
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47 if npoints == 1
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48 xneworigo = xwedge(1,:);
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49
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50 xknown1 = xwedge(2,:) - xneworigo;
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51 xknown1 = xknown1 / norm(xknown1);
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52
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53 A = [nvec1(2)*xknown1(3)-nvec1(3)*xknown1(2) ; nvec1(3)*xknown1(1)-nvec1(1)*xknown1(3) ; nvec1(1)*xknown1(2)-nvec1(2)*xknown1(1)];
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54 A = inv([xknown1.' A nvec1.']);
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55
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56 xsou = (A([2 3 1],:)*( xsou.' - xneworigo.' )).';
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57
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58 rs = norm(xsou(1:2));
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59 zs = xsou(:,3);
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60 thetas = 0;
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61 if rs > 0
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62 thetas = real( acos( xsou(1)./rs ).*( xsou(2) ~= 0) );
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63 thetas = thetas + pi*( (xsou(2)==0) & xsou(1) < 0 );
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64 thetas = thetas.*( xsou(2) >=0 ) + (2*pi - thetas).*( xsou(2) < 0 );
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65 end
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66
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67 else
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68 xneworigo = xwedge(1,:);
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69
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70 xknown1 = xwedge(2,:) - xneworigo;
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71 xknown1 = xknown1 / sqrt( sum( xknown1.^2 ));
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72
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73
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74 A = [0 1 0;0 0 1;1 0 0]*inv([xknown1.' EDB1cross(nvec1.',xknown1.') nvec1.']);
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75
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76 [npoints,slask] = size(xsou);
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77 xsou = (A*( xsou.' - xneworigo(ones(npoints,1),:).' )).';
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78
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79 rs = sqrt( sum(xsou(:,1:2).'.^2) ).';
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80 zs = xsou(:,3);
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81 thetas = zeros(npoints,1);
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82 iv = find(rs>0);
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83 if ~isempty(iv)
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84 thetas(iv) = real( acos( xsou(iv,1)./rs(iv) ).*( xsou(iv,2) ~= 0) );
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85 thetas(iv) = thetas(iv) + pi*( (xsou(iv,2)==0) & xsou(iv,1) < 0 );
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86 thetas(iv) = thetas(iv).*( xsou(iv,2) >=0 ) + (2*pi - thetas(iv)).*( xsou(iv,2) < 0 );
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87 end
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88
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89 end |
