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annotate +parametrization/Ti3D.m @ 774:66eb4a2bbb72 feature/grids

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Remove default scaling of the system. The scaling doens't seem to help actual solutions. One example that fails in the flexural code. With large timesteps the solutions seems to blow up. One particular example is profilePresentation on the tdb_presentation_figures branch with k = 0.0005
author Jonatan Werpers <jonatan@werpers.com>
date Wed, 18 Jul 2018 15:42:52 -0700
parents eef74cd9b49c
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 classdef Ti3D
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2 properties
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3 gs % {6}Surfaces
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4 V % FunctionHandle(XI,ETA,ZETA)
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5 end
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6
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7 methods
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8 % TODO write all fancy features for flipping around with the surfaces
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9 % Each surface is defined with an outward facing outward and choosing
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10 % the "corner" where XI=0 if not possible the corner where ETA=0 is choosen
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11 function obj = Ti3D(CW,CE,CS,CN,CB,CT)
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12 obj.gs = {CE,CW,CS,CN,CB,CT};
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13
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14 gw = CW.g;
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15 ge = CE.g;
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16 gs = CS.g;
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17 gn = CN.g;
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18 gb = CB.g;
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19 gt = CT.g;
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20
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21 function o = V_fun(XI,ETA,ZETA)
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22 XI=XI';
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23 ETA=ETA';
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24 ZETA=ZETA';
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26 one=0*ETA+1;
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27 zero=0*ETA;
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28
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29 Sw = gw(ETA,(1-ZETA));
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30 Se = ge((1-ETA),(1-ZETA));
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31 Ss = gs(XI,ZETA);
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32 Sn = gn((1-XI),(1-ZETA));
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33 Sb = gb((1-XI),ETA);
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34 St = gt(XI,ETA);
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35
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36 Ewt = gw(ETA,zero);
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37 Ewb = gw(ETA,one);
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38 Ews = gw(zero,1-ZETA);
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39 Ewn = gw(one,1-ZETA);
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40 Eet = ge(1-ETA,zero);
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41 Eeb = ge(1-ETA,one);
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42 Ees = ge(one,1-ZETA);
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43 Een = ge(zero,1-ZETA);
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44 Enb = gn(1-XI,one);
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45 Ent = gn(1-XI,zero);
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46 Est = gs(XI,one);
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47 Esb = gs(XI,zero);
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48
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49 Cwbs = gw(zero,one);
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50 Cwbn = gw(one,one);
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51 Cwts = gw(zero,zero);
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52 Cwtn = gw(one,zero);
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53 Cebs = ge(one,one);
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54 Cebn = ge(zero,one);
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55 Cets = ge(one,zero);
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56 Cetn = ge(zero,zero);
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59 X1 = (1-XI).*Sw(1,:,:) + XI.*Se(1,:,:);
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60 X2 = (1-ETA).*Ss(1,:,:) + ETA.*Sn(1,:,:);
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61 X3 = (1-ZETA).*Sb(1,:,:) + ZETA.*St(1,:,:);
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62
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63 X12 = (1-XI).*(1-ETA).*Ews(1,:,:) + (1-XI).*ETA.*Ewn(1,:,:) + XI.*(1-ETA).*Ees(1,:,:) + XI.*ETA.*Een(1,:,:);
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64 X13 = (1-XI).*(1-ZETA).*Ewb(1,:,:) + (1-XI).*ZETA.*Ewt(1,:,:) + XI.*(1-ZETA).*Eeb(1,:,:) + XI.*ZETA.*Eet(1,:,:);
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65 X23 = (1-ETA).*(1-ZETA).*Esb(1,:,:) + (1-ETA).*ZETA.*Est(1,:,:) + ETA.*(1-ZETA).*Enb(1,:,:) + ETA.*ZETA.*Ent(1,:,:);
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67 X123 = (1-XI).*(1-ETA).*(1-ZETA).*Cwbs(1,:,:) + (1-XI).*(1-ETA).*ZETA.*Cwts(1,:,:) + (1-XI).*ETA.*(1-ZETA).*Cwbn(1,:,:) + ...
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68 (1-XI).*ETA.*ZETA.*Cwtn(1,:,:) + XI.*(1-ETA).*(1-ZETA).*Cebs(1,:,:) + XI.*(1-ETA).*ZETA.*Cets(1,:,:) + ...
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69 XI.*ETA.*(1-ZETA).*Cebn(1,:,:) + XI.*ETA.*ZETA.*Cetn(1,:,:);
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71 X = X1 + X2 + X3 - X12 - X13 - X23 + X123;
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74 Y1 = (1-XI).*Sw(2,:,:) + XI.*Se(2,:,:);
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75 Y2 = (1-ETA).*Ss(2,:,:) + ETA.*Sn(2,:,:);
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76 Y3 = (1-ZETA).*Sb(2,:,:) + ZETA.*St(2,:,:);
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77
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78 Y12 = (1-XI).*(1-ETA).*Ews(2,:,:) + (1-XI).*ETA.*Ewn(2,:,:) + XI.*(1-ETA).*Ees(2,:,:) + XI.*ETA.*Een(2,:,:);
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79 Y13 = (1-XI).*(1-ZETA).*Ewb(2,:,:) + (1-XI).*ZETA.*Ewt(2,:,:) + XI.*(1-ZETA).*Eeb(2,:,:) + XI.*ZETA.*Eet(2,:,:);
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80 Y23 = (1-ETA).*(1-ZETA).*Esb(2,:,:) + (1-ETA).*ZETA.*Est(2,:,:) + ETA.*(1-ZETA).*Enb(2,:,:) + ETA.*ZETA.*Ent(2,:,:);
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81
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82 Y123 = (1-XI).*(1-ETA).*(1-ZETA).*Cwbs(2,:,:) + (1-XI).*(1-ETA).*ZETA.*Cwts(2,:,:) + (1-XI).*ETA.*(1-ZETA).*Cwbn(2,:,:) + ...
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83 (1-XI).*ETA.*ZETA.*Cwtn(2,:,:) + XI.*(1-ETA).*(1-ZETA).*Cebs(2,:,:) + XI.*(1-ETA).*ZETA.*Cets(2,:,:) + ...
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84 XI.*ETA.*(1-ZETA).*Cebn(2,:,:) + XI.*ETA.*ZETA.*Cetn(2,:,:);
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86 Y = Y1 + Y2 + Y3 - Y12 - Y13 - Y23 + Y123;
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89 Z1 = (1-XI).*Sw(3,:,:) + XI.*Se(3,:,:);
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90 Z2 = (1-ETA).*Ss(3,:,:) + ETA.*Sn(3,:,:);
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91 Z3 = (1-ZETA).*Sb(3,:,:) + ZETA.*St(3,:,:);
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92
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93 Z12 = (1-XI).*(1-ETA).*Ews(3,:,:) + (1-XI).*ETA.*Ewn(3,:,:) + XI.*(1-ETA).*Ees(3,:,:) + XI.*ETA.*Een(3,:,:);
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94 Z13 = (1-XI).*(1-ZETA).*Ewb(3,:,:) + (1-XI).*ZETA.*Ewt(3,:,:) + XI.*(1-ZETA).*Eeb(3,:,:) + XI.*ZETA.*Eet(3,:,:);
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95 Z23 = (1-ETA).*(1-ZETA).*Esb(3,:,:) + (1-ETA).*ZETA.*Est(3,:,:) + ETA.*(1-ZETA).*Enb(3,:,:) + ETA.*ZETA.*Ent(3,:,:);
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97 Z123 = (1-XI).*(1-ETA).*(1-ZETA).*Cwbs(3,:,:) + (1-XI).*(1-ETA).*ZETA.*Cwts(3,:,:) + (1-XI).*ETA.*(1-ZETA).*Cwbn(3,:,:) + ...
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98 (1-XI).*ETA.*ZETA.*Cwtn(3,:,:) + XI.*(1-ETA).*(1-ZETA).*Cebs(3,:,:) + XI.*(1-ETA).*ZETA.*Cets(3,:,:) + ...
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99 XI.*ETA.*(1-ZETA).*Cebn(3,:,:) + XI.*ETA.*ZETA.*Cetn(3,:,:);
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101 Z = Z1 + Z2 + Z3 - Z12 - Z13 - Z23 + Z123;
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102 o = [X;Y;Z];
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103 end
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104
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105 obj.V = @V_fun;
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106 end
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107
350
5d5652fe826a A commit before I try resolving the performance issues
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108 %Should be rewritten so that the input is xi eta zeta
349
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109 function [X,Y,Z] = map(obj,XI,ETA,ZETA)
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110
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111 V = obj.V;
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112
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113 p = V(XI,ETA,ZETA);
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114 X = p(1,:)';
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115 Y = p(2,:)';
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116 Z = p(3,:)';
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117
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118 end
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119
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120 % function h = plot(obj,nu,nv)
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121 % S = obj.S;
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122 %
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123 % default_arg('nv',nu)
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124 %
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125 % u = linspace(0,1,nu);
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126 % v = linspace(0,1,nv);
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127 %
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128 % m = 100;
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129 %
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130 % X = zeros(nu+nv,m);
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131 % Y = zeros(nu+nv,m);
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132 %
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133 %
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134 % t = linspace(0,1,m);
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135 % for i = 1:nu
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136 % p = S(u(i),t);
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137 % X(i,:) = p(1,:);
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138 % Y(i,:) = p(2,:);
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139 % end
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140 %
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141 % for i = 1:nv
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142 % p = S(t,v(i));
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143 % X(i+nu,:) = p(1,:);
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144 % Y(i+nu,:) = p(2,:);
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145 % end
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146 %
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147 % h = line(X',Y');
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148 % end
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149 %
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150 %
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151 % function h = show(obj,nu,nv)
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152 % default_arg('nv',nu)
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153 % S = obj.S;
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154 %
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155 % if(nu>2 || nv>2)
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156 % h_grid = obj.plot(nu,nv);
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157 % set(h_grid,'Color',[0 0.4470 0.7410]);
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158 % end
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159 %
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160 % h_bord = obj.plot(2,2);
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161 % set(h_bord,'Color',[0.8500 0.3250 0.0980]);
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162 % set(h_bord,'LineWidth',2);
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163 % end
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164 %
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165 %
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166 % % TRANSFORMATIONS
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167 % function ti = translate(obj,a)
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168 % gs = obj.gs;
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169 %
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170 % for i = 1:length(gs)
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171 % new_gs{i} = gs{i}.translate(a);
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172 % end
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173 %
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174 % ti = grid.Ti(new_gs{:});
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175 % end
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176 %
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177 % % Mirrors the Ti so that the resulting Ti is still left handed.
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178 % % (Corrected by reversing curves and switching e and w)
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179 % function ti = mirror(obj, a, b)
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180 % gs = obj.gs;
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181 %
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182 % new_gs = cell(1,4);
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183 %
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184 % new_gs{1} = gs{1}.mirror(a,b).reverse();
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185 % new_gs{3} = gs{3}.mirror(a,b).reverse();
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186 % new_gs{2} = gs{4}.mirror(a,b).reverse();
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187 % new_gs{4} = gs{2}.mirror(a,b).reverse();
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188 %
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189 % ti = grid.Ti(new_gs{:});
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190 % end
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191 %
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192 % function ti = rotate(obj,a,rad)
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193 % gs = obj.gs;
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194 %
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195 % for i = 1:length(gs)
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196 % new_gs{i} = gs{i}.rotate(a,rad);
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197 % end
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198 %
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199 % ti = grid.Ti(new_gs{:});
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200 % end
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201 %
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202 % function ti = rotate_edges(obj,n);
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203 % new_gs = cell(1,4);
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204 % for i = 0:3
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205 % new_i = mod(i - n,4);
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206 % new_gs{new_i+1} = obj.gs{i+1};
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207 % end
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208 % ti = grid.Ti(new_gs{:});
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209 % end
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210 % end
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211 %
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212 % methods(Static)
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213 % function obj = points(p1, p2, p3, p4)
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214 % g1 = grid.Curve.line(p1,p2);
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215 % g2 = grid.Curve.line(p2,p3);
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216 % g3 = grid.Curve.line(p3,p4);
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217 % g4 = grid.Curve.line(p4,p1);
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218 %
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219 % obj = grid.Ti(g1,g2,g3,g4);
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220 % end
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221 %
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222 % function label(varargin)
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223 % if nargin == 2 && ischar(varargin{2})
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224 % label_impl(varargin{:});
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225 % else
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226 % for i = 1:length(varargin)
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227 % label_impl(varargin{i},inputname(i));
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228 % end
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229 % end
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230 %
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231 %
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232 % function label_impl(ti,str)
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233 % S = ti.S;
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234 %
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235 % pc = S(0.5,0.5);
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236 %
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237 % margin = 0.1;
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238 % pw = S( margin, 0.5);
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239 % pe = S(1-margin, 0.5);
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240 % ps = S( 0.5, margin);
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241 % pn = S( 0.5, 1-margin);
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242 %
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243 %
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244 % ti.show(2,2);
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245 % grid.place_label(pc,str);
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246 % grid.place_label(pw,'w');
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247 % grid.place_label(pe,'e');
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248 % grid.place_label(ps,'s');
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249 % grid.place_label(pn,'n');
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250 % end
350
5d5652fe826a A commit before I try resolving the performance issues
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251 % end
349
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252 end
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253 end