Hi,

I have been trying to set the geometry in ThreeDCircularProjectionGeometry
with values between 0 and 180 degrees, to reproduce the motion of some
acquisition systems, but reconstruction is far from the expected result
when the gantry angle does not reach max value of (360-increment).
(Attached is the geometry file generated)

My workflow is the following :

   - Apply JosephForwardProjectionImageFilter on a 3D Volume
   - Try to reconstruct using FDKConeBeamReconstructionFilter

Although, the result from JosephForwardProjectionImageFilter describes a
180 degrees rotation, the output of the reconstruction seems to display
rays from opposite direction but not from rotated directions


Here is a view of what is supposed to be an axial slice:

[image: image.png]

Thanks for your help!

Clément
<?xml version="1.0"?>
<!DOCTYPE RTKGEOMETRY>
<RTKThreeDCircularGeometry version="3">
    <SourceToIsocenterDistance>600</SourceToIsocenterDistance>
    <SourceToDetectorDistance>1200</SourceToDetectorDistance>
  <Projection>
    <GantryAngle>0</GantryAngle>
    <Matrix>
                    -1200                   0                   0                   0
                        0               -1200                   0                   0
                        0                   0                   1                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>2</GantryAngle>
    <Matrix>
        -1199.26899242291                   0    41.8793960430012                   0
                        0               -1200                   0                   0
        0.034899496702501                   0   0.999390827019096                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>4</GantryAngle>
    <Matrix>
        -1197.07686031179                   0    83.7077684929504                   0
                        0               -1200                   0                   0
       0.0697564737441253                   0   0.997564050259824                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>6</GantryAngle>
    <Matrix>
        -1193.42627444193                   0    125.434155921184                   0
                        0               -1200                   0                   0
        0.104528463267653                   0   0.994521895368273                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>8</GantryAngle>
    <Matrix>
        -1188.32168248988                   0    167.007721152079                   0
                        0               -1200                   0                   0
        0.139173100960065                   0    0.99026806874157                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>10</GantryAngle>
    <Matrix>
        -1181.76930361465                   0    208.377813200316                   0
                        0               -1200                   0                   0
         0.17364817766693                   0   0.984807753012208                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>12</GantryAngle>
    <Matrix>
        -1173.77712088057                   0    249.494028981311                   0
                        0               -1200                   0                   0
        0.207911690817759                   0   0.978147600733806                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>14</GantryAngle>
    <Matrix>
         -1164.3548715312                   0    290.306274719601                   0
                        0               -1200                   0                   0
        0.241921895599668                   0   0.970295726275996                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>16</GantryAngle>
    <Matrix>
        -1153.51403512598                   0    330.764826980399                   0
                        0               -1200                   0                   0
        0.275637355816999                   0   0.961261695938319                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>18</GantryAngle>
    <Matrix>
        -1141.26781955418                   0    370.820393249937                   0
                        0               -1200                   0                   0
        0.309016994374947                   0   0.951056516295154                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>20</GantryAngle>
    <Matrix>
        -1127.63114494309                   0    410.424171990802                   0
                        0               -1200                   0                   0
        0.342020143325669                   0   0.939692620785908                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>22</GantryAngle>
    <Matrix>
        -1112.62062548015                   0    449.527912099094                   0
                        0               -1200                   0                   0
        0.374606593415912                   0   0.927183854566787                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>24</GantryAngle>
    <Matrix>
        -1096.25454917112                   0     488.08397169096                   0
                        0               -1200                   0                   0
          0.4067366430758                   0   0.913545457642601                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>26</GantryAngle>
    <Matrix>
          -1078.552855559                   0    526.045376146893                   0
                        0               -1200                   0                   0
        0.438371146789077                   0   0.898794046299167                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>28</GantryAngle>
    <Matrix>
        -1059.53711143071                   0    563.365875343069                   0
                        0               -1200                   0                   0
        0.469471562785891                   0   0.882947592858927                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>30</GantryAngle>
    <Matrix>
        -1039.23048454133                   0                 600                   0
                        0               -1200                   0                   0
                      0.5                   0   0.866025403784439                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>32</GantryAngle>
    <Matrix>
        -1017.65771538771                   0    635.903117079846                   0
                        0               -1200                   0                   0
        0.529919264233205                   0   0.848048096156426                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>34</GantryAngle>
    <Matrix>
         -994.84508706605                   0    671.031484164896                   0
                        0               -1200                   0                   0
        0.559192903470747                   0   0.829037572555042                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>36</GantryAngle>
    <Matrix>
        -970.820393249937                   0    705.342302750968                   0
                        0               -1200                   0                   0
        0.587785252292473                   0   0.809016994374947                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>38</GantryAngle>
    <Matrix>
        -945.612904328066                   0     738.79377039079                   0
                        0               -1200                   0                   0
        0.615661475325658                   0   0.788010753606722                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>40</GantryAngle>
    <Matrix>
        -919.253331742774                   0    771.345131623847                   0
                        0               -1200                   0                   0
        0.642787609686539                   0   0.766044443118978                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>42</GantryAngle>
    <Matrix>
        -891.773790572873                   0     802.95672763063                   0
                        0               -1200                   0                   0
        0.669130606358858                   0   0.743144825477394                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>44</GantryAngle>
    <Matrix>
        -863.207760406381                   0    833.590044550797                   0
                        0               -1200                   0                   0
        0.694658370458997                   0   0.719339800338651                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>46</GantryAngle>
    <Matrix>
        -833.590044550797                   0    863.207760406381                   0
                        0               -1200                   0                   0
        0.719339800338651                   0   0.694658370458997                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>48</GantryAngle>
    <Matrix>
         -802.95672763063                   0    891.773790572873                   0
                        0               -1200                   0                   0
        0.743144825477394                   0   0.669130606358858                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>50</GantryAngle>
    <Matrix>
        -771.345131623847                   0    919.253331742774                   0
                        0               -1200                   0                   0
        0.766044443118978                   0   0.642787609686539                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>52</GantryAngle>
    <Matrix>
         -738.79377039079                   0    945.612904328066                   0
                        0               -1200                   0                   0
        0.788010753606722                   0   0.615661475325658                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>54</GantryAngle>
    <Matrix>
        -705.342302750968                   0    970.820393249937                   0
                        0               -1200                   0                   0
        0.809016994374947                   0   0.587785252292473                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>56</GantryAngle>
    <Matrix>
        -671.031484164896                   0     994.84508706605                   0
                        0               -1200                   0                   0
        0.829037572555042                   0   0.559192903470747                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>58</GantryAngle>
    <Matrix>
        -635.903117079846                   0    1017.65771538771                   0
                        0               -1200                   0                   0
        0.848048096156426                   0   0.529919264233205                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>60</GantryAngle>
    <Matrix>
                     -600                   0    1039.23048454133                   0
                        0               -1200                   0                   0
        0.866025403784439                   0                 0.5                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>62</GantryAngle>
    <Matrix>
        -563.365875343069                   0    1059.53711143071                   0
                        0               -1200                   0                   0
        0.882947592858927                   0   0.469471562785891                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>64</GantryAngle>
    <Matrix>
        -526.045376146893                   0      1078.552855559                   0
                        0               -1200                   0                   0
        0.898794046299167                   0   0.438371146789077                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>66</GantryAngle>
    <Matrix>
         -488.08397169096                   0    1096.25454917112                   0
                        0               -1200                   0                   0
        0.913545457642601                   0     0.4067366430758                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>68</GantryAngle>
    <Matrix>
        -449.527912099094                   0    1112.62062548015                   0
                        0               -1200                   0                   0
        0.927183854566787                   0   0.374606593415912                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>70</GantryAngle>
    <Matrix>
        -410.424171990803                   0    1127.63114494309                   0
                        0               -1200                   0                   0
        0.939692620785908                   0   0.342020143325669                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>72</GantryAngle>
    <Matrix>
        -370.820393249937                   0    1141.26781955418                   0
                        0               -1200                   0                   0
        0.951056516295154                   0   0.309016994374947                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>74</GantryAngle>
    <Matrix>
        -330.764826980399                   0    1153.51403512598                   0
                        0               -1200                   0                   0
        0.961261695938319                   0   0.275637355816999                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>76</GantryAngle>
    <Matrix>
        -290.306274719601                   0     1164.3548715312                   0
                        0               -1200                   0                   0
        0.970295726275996                   0   0.241921895599668                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>78</GantryAngle>
    <Matrix>
        -249.494028981311                   0    1173.77712088057                   0
                        0               -1200                   0                   0
        0.978147600733806                   0   0.207911690817759                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>80</GantryAngle>
    <Matrix>
        -208.377813200316                   0    1181.76930361465                   0
                        0               -1200                   0                   0
        0.984807753012208                   0    0.17364817766693                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>82</GantryAngle>
    <Matrix>
        -167.007721152079                   0    1188.32168248988                   0
                        0               -1200                   0                   0
         0.99026806874157                   0   0.139173100960065                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>84</GantryAngle>
    <Matrix>
        -125.434155921184                   0    1193.42627444193                   0
                        0               -1200                   0                   0
        0.994521895368273                   0   0.104528463267653                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>86</GantryAngle>
    <Matrix>
        -83.7077684929503                   0    1197.07686031179                   0
                        0               -1200                   0                   0
        0.997564050259824                   0  0.0697564737441252                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>88</GantryAngle>
    <Matrix>
        -41.8793960430013                   0    1199.26899242291                   0
                        0               -1200                   0                   0
        0.999390827019096                   0  0.0348994967025011                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>90</GantryAngle>
    <Matrix>
      -7.34788079488412e-14                   0                1200                   0
                        0               -1200                   0                   0
                        1                   0 6.12323399573677e-17                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>92</GantryAngle>
    <Matrix>
         41.8793960430011                   0    1199.26899242291                   0
                        0               -1200                   0                   0
        0.999390827019096                   0  -0.034899496702501                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>94</GantryAngle>
    <Matrix>
         83.7077684929504                   0    1197.07686031179                   0
                        0               -1200                   0                   0
        0.997564050259824                   0 -0.0697564737441253                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>96</GantryAngle>
    <Matrix>
         125.434155921184                   0    1193.42627444193                   0
                        0               -1200                   0                   0
        0.994521895368273                   0  -0.104528463267654                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>98</GantryAngle>
    <Matrix>
         167.007721152078                   0    1188.32168248988                   0
                        0               -1200                   0                   0
         0.99026806874157                   0  -0.139173100960065                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>100</GantryAngle>
    <Matrix>
         208.377813200316                   0    1181.76930361465                   0
                        0               -1200                   0                   0
        0.984807753012208                   0   -0.17364817766693                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>102</GantryAngle>
    <Matrix>
         249.494028981311                   0    1173.77712088057                   0
                        0               -1200                   0                   0
        0.978147600733806                   0  -0.207911690817759                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>104</GantryAngle>
    <Matrix>
         290.306274719601                   0     1164.3548715312                   0
                        0               -1200                   0                   0
        0.970295726275996                   0  -0.241921895599668                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>106</GantryAngle>
    <Matrix>
         330.764826980399                   0    1153.51403512598                   0
                        0               -1200                   0                   0
        0.961261695938319                   0  -0.275637355816999                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>108</GantryAngle>
    <Matrix>
         370.820393249937                   0    1141.26781955418                   0
                        0               -1200                   0                   0
        0.951056516295154                   0  -0.309016994374947                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>110</GantryAngle>
    <Matrix>
         410.424171990802                   0    1127.63114494309                   0
                        0               -1200                   0                   0
        0.939692620785908                   0  -0.342020143325669                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>112</GantryAngle>
    <Matrix>
         449.527912099094                   0    1112.62062548015                   0
                        0               -1200                   0                   0
        0.927183854566787                   0  -0.374606593415912                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>114</GantryAngle>
    <Matrix>
          488.08397169096                   0    1096.25454917112                   0
                        0               -1200                   0                   0
        0.913545457642601                   0    -0.4067366430758                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>116</GantryAngle>
    <Matrix>
         526.045376146893                   0      1078.552855559                   0
                        0               -1200                   0                   0
        0.898794046299167                   0  -0.438371146789078                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>118</GantryAngle>
    <Matrix>
         563.365875343069                   0    1059.53711143071                   0
                        0               -1200                   0                   0
        0.882947592858927                   0  -0.469471562785891                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>120</GantryAngle>
    <Matrix>
                      600                   0    1039.23048454133                   0
                        0               -1200                   0                   0
        0.866025403784439                   0                -0.5                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>122</GantryAngle>
    <Matrix>
         635.903117079846                   0    1017.65771538771                   0
                        0               -1200                   0                   0
        0.848048096156426                   0  -0.529919264233205                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>124</GantryAngle>
    <Matrix>
         671.031484164896                   0     994.84508706605                   0
                        0               -1200                   0                   0
        0.829037572555042                   0  -0.559192903470747                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>126</GantryAngle>
    <Matrix>
         705.342302750968                   0    970.820393249937                   0
                        0               -1200                   0                   0
        0.809016994374947                   0  -0.587785252292473                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>128</GantryAngle>
    <Matrix>
          738.79377039079                   0    945.612904328066                   0
                        0               -1200                   0                   0
        0.788010753606722                   0  -0.615661475325658                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>130</GantryAngle>
    <Matrix>
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        0.766044443118978                   0  -0.642787609686539                -600
    </Matrix>
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    <GantryAngle>132</GantryAngle>
    <Matrix>
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    </Matrix>
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    <GantryAngle>134</GantryAngle>
    <Matrix>
         833.590044550797                   0    863.207760406381                   0
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    </Matrix>
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    <GantryAngle>136</GantryAngle>
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    </Matrix>
  </Projection>
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    <GantryAngle>138</GantryAngle>
    <Matrix>
         891.773790572873                   0     802.95672763063                   0
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    </Matrix>
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    <GantryAngle>140</GantryAngle>
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         919.253331742774                   0    771.345131623847                   0
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    </Matrix>
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    <GantryAngle>142</GantryAngle>
    <Matrix>
         945.612904328066                   0     738.79377039079                   0
                        0               -1200                   0                   0
        0.615661475325658                   0  -0.788010753606722                -600
    </Matrix>
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    <GantryAngle>144</GantryAngle>
    <Matrix>
         970.820393249937                   0    705.342302750968                   0
                        0               -1200                   0                   0
        0.587785252292473                   0  -0.809016994374947                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>146</GantryAngle>
    <Matrix>
          994.84508706605                   0    671.031484164896                   0
                        0               -1200                   0                   0
        0.559192903470747                   0  -0.829037572555042                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>148</GantryAngle>
    <Matrix>
         1017.65771538771                   0    635.903117079846                   0
                        0               -1200                   0                   0
        0.529919264233205                   0  -0.848048096156426                -600
    </Matrix>
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  <Projection>
    <GantryAngle>150</GantryAngle>
    <Matrix>
         1039.23048454133                   0                 600                   0
                        0               -1200                   0                   0
                      0.5                   0  -0.866025403784439                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>152</GantryAngle>
    <Matrix>
         1059.53711143071                   0    563.365875343069                   0
                        0               -1200                   0                   0
        0.469471562785891                   0  -0.882947592858927                -600
    </Matrix>
  </Projection>
  <Projection>
    <GantryAngle>154</GantryAngle>
    <Matrix>
           1078.552855559                   0    526.045376146893                   0
                        0               -1200                   0                   0
        0.438371146789077                   0  -0.898794046299167                -600
    </Matrix>
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  <Projection>
    <GantryAngle>156</GantryAngle>
    <Matrix>
         1096.25454917112                   0    488.083971690961                   0
                        0               -1200                   0                   0
          0.4067366430758                   0  -0.913545457642601                -600
    </Matrix>
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  <Projection>
    <GantryAngle>158</GantryAngle>
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    <GantryAngle>160</GantryAngle>
    <Matrix>
         1127.63114494309                   0    410.424171990803                   0
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        0.342020143325669                   0  -0.939692620785908                -600
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  <Projection>
    <GantryAngle>162</GantryAngle>
    <Matrix>
         1141.26781955418                   0    370.820393249937                   0
                        0               -1200                   0                   0
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  <Projection>
    <GantryAngle>164</GantryAngle>
    <Matrix>
         1153.51403512598                   0    330.764826980399                   0
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    <GantryAngle>166</GantryAngle>
    <Matrix>
          1164.3548715312                   0    290.306274719601                   0
                        0               -1200                   0                   0
        0.241921895599668                   0  -0.970295726275996                -600
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  <Projection>
    <GantryAngle>168</GantryAngle>
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         1173.77712088057                   0    249.494028981311                   0
                        0               -1200                   0                   0
        0.207911690817759                   0  -0.978147600733806                -600
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    <GantryAngle>170</GantryAngle>
    <Matrix>
         1181.76930361465                   0    208.377813200316                   0
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         0.17364817766693                   0  -0.984807753012208                -600
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  <Projection>
    <GantryAngle>172</GantryAngle>
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         1188.32168248988                   0    167.007721152078                   0
                        0               -1200                   0                   0
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    <GantryAngle>174</GantryAngle>
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    <GantryAngle>176</GantryAngle>
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         1197.07686031179                   0    83.7077684929506                   0
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</RTKThreeDCircularGeometry>
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