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1 classdef Ti
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2 properties
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3 gs % {4}Curve
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4 S % FunctionHandle(u,v)
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5 end
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6
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7 methods
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8 % TODO function to label boundary names.
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9 % function to find largest and smallest delta h in the grid. Maybe shouldnt live here
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10 function obj = Ti(C1,C2,C3,C4)
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11 obj.gs = {C1,C2,C3,C4};
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12
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13 g1 = C1.g;
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14 g2 = C2.g;
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15 g3 = C3.g;
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16 g4 = C4.g;
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17
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18 A = g1(0);
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19 B = g2(0);
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20 C = g3(0);
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21 D = g4(0);
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22
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23 function o = S_fun(u,v)
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24 x1 = g1(u);
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25 x2 = g2(v);
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26 x3 = g3(1-u);
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27 x4 = g4(1-v);
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28 o1 = (1-v).*x1(1,:) + u.*x2(1,:) + v.*x3(1,:) + (1-u).*x4(1,:) ...
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29 -((1-u)*(1-v).*A(1,:) + u*(1-v).*B(1,:) + u*v.*C(1,:) + (1-u)*v.*D(1,:));
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30 o2 = (1-v).*x1(2,:) + u.*x2(2,:) + v.*x3(2,:) + (1-u).*x4(2,:) ...
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31 -((1-u)*(1-v).*A(2,:) + u*(1-v).*B(2,:) + u*v.*C(2,:) + (1-u)*v.*D(2,:));
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32
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33 o = [o1;o2];
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34 end
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35
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36 obj.S = @S_fun;
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37 end
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38
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39 function [X,Y] = map(obj,u,v)
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40 default_arg('v',u);
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41
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42 if isscalar(u)
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43 u = linspace(0,1,u);
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44 end
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45
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46 if isscalar(v)
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47 v = linspace(0,1,v);
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48 end
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49
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50 S = obj.S;
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51
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52 nu = length(u);
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53 nv = length(v);
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54
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55 X = zeros(nv,nu);
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56 Y = zeros(nv,nu);
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57
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58 u = rowVector(u);
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59 v = rowVector(v);
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60
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61 for i = 1:nv
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62 p = S(u,v(i));
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63 X(i,:) = p(1,:);
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64 Y(i,:) = p(2,:);
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65 end
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66 end
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67
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68 function h = plot(obj,nu,nv)
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69 S = obj.S;
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70
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71 default_arg('nv',nu)
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72
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73 u = linspace(0,1,nu);
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74 v = linspace(0,1,nv);
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75
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76 m = 100;
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77
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78 X = zeros(nu+nv,m);
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79 Y = zeros(nu+nv,m);
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80
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81
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82 t = linspace(0,1,m);
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83 for i = 1:nu
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84 p = S(u(i),t);
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85 X(i,:) = p(1,:);
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86 Y(i,:) = p(2,:);
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87 end
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88
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89 for i = 1:nv
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90 p = S(t,v(i));
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91 X(i+nu,:) = p(1,:);
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92 Y(i+nu,:) = p(2,:);
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93 end
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94
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95 h = line(X',Y');
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96 end
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97
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98
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99 function h = show(obj,nu,nv)
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100 default_arg('nv',nu)
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101 S = obj.S;
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102
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103 if(nu>2 || nv>2)
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104 h_grid = obj.plot(nu,nv);
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105 set(h_grid,'Color',[0 0.4470 0.7410]);
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106 end
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107
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108 h_bord = obj.plot(2,2);
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109 set(h_bord,'Color',[0.8500 0.3250 0.0980]);
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110 set(h_bord,'LineWidth',2);
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111 end
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112
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113
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114 % TRANSFORMATIONS
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115 function ti = translate(obj,a)
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116 gs = obj.gs;
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117
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118 for i = 1:length(gs)
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119 new_gs{i} = gs{i}.translate(a);
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120 end
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121
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122 ti = grid.Ti(new_gs{:});
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123 end
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124
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125 % Mirrors the Ti so that the resulting Ti is still left handed.
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126 % (Corrected by reversing curves and switching e and w)
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127 function ti = mirror(obj, a, b)
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128 gs = obj.gs;
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129
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130 new_gs = cell(1,4);
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131
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132 new_gs{1} = gs{1}.mirror(a,b).reverse();
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133 new_gs{3} = gs{3}.mirror(a,b).reverse();
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134 new_gs{2} = gs{4}.mirror(a,b).reverse();
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135 new_gs{4} = gs{2}.mirror(a,b).reverse();
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136
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137 ti = grid.Ti(new_gs{:});
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138 end
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139
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140 function ti = rotate(obj,a,rad)
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141 gs = obj.gs;
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142
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143 for i = 1:length(gs)
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144 new_gs{i} = gs{i}.rotate(a,rad);
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145 end
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146
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147 ti = grid.Ti(new_gs{:});
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148 end
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149
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150 function ti = rotate_edges(obj,n);
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151 new_gs = cell(1,4);
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152 for i = 0:3
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153 new_i = mod(i - n,4);
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154 new_gs{new_i+1} = obj.gs{i+1};
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155 end
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156 ti = grid.Ti(new_gs{:});
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157 end
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158 end
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159
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160 methods(Static)
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161 function obj = points(p1, p2, p3, p4)
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162 g1 = grid.Curve.line(p1,p2);
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163 g2 = grid.Curve.line(p2,p3);
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164 g3 = grid.Curve.line(p3,p4);
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165 g4 = grid.Curve.line(p4,p1);
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166
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167 obj = grid.Ti(g1,g2,g3,g4);
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168 end
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169
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170 function label(varargin)
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171 if nargin == 2 && ischar(varargin{2})
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172 label_impl(varargin{:});
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173 else
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174 for i = 1:length(varargin)
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175 label_impl(varargin{i},inputname(i));
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176 end
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177 end
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178
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179
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180 function label_impl(ti,str)
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181 S = ti.S;
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182
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183 pc = S(0.5,0.5);
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184
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185 margin = 0.1;
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186 pw = S( margin, 0.5);
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187 pe = S(1-margin, 0.5);
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188 ps = S( 0.5, margin);
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189 pn = S( 0.5, 1-margin);
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190
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191
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192 ti.show(2,2);
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193 grid.place_label(pc,str);
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194 grid.place_label(pw,'w');
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195 grid.place_label(pe,'e');
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196 grid.place_label(ps,'s');
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197 grid.place_label(pn,'n');
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198 end
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199 end
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200 end
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201 end |
