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85 <p><img src="../i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> Smoothing is used to adjust the locations of element
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86 corners (nodes) to reduce distortions in these elements.</p>
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90 <p class=TODO>To apply smoothing to the elements of your mesh:</p>
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94 <p class="whs2">1. Display a mesh or a submesh in the 3D
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97 <p class="whs2">2. In the <span style="font-weight: bold;"><B>Modification
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98 </B></span>menu select the <span style="font-weight: bold;"><B>Smoothing </B></span>item
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99 or click <img src="../image84.gif" width="24px" height="25px" border="0" class="img_whs3"> button in the toolbar. The <span style="margin-left: 40px;">dialog
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100 box contains the following fields which should be specified:</span></p>
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104 <p class="whs2"><img src="../pics/smoothing.png" x-maintain-ratio="TRUE" width="332px" height="396px" border="0" class="img_whs4"> </p>
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106 <ul type="disc" class="whs5">
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108 <li class=kadov-p><p class="whs6"><span
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109 style="font-weight: bold;"><B>Id Elements </B></span><span>field allows to specify
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110 the elements which should be smoothed by selecting them in the 3D viewer.
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111 Note: to select several elements press </span><span style="font-weight: bold;"><B>Shift
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112 </B></span><span>button.</span></p></li>
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114 <ul type="disc" class="whs5">
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116 <li class=kadov-p><p class="whs7">Smoothing is applied
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117 to the whole mesh or its part</p></li>
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119 <li class=kadov-p><p><span style="font-weight: bold;"><B>Fixed nodes
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120 ids</B></span>: some nodes keep their location during smoothing. If a mesh
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121 is built on a geometry shape, the nodes built on geometrical edges are
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122 always fixed. If smoothing is applied to a part of a mesh then the boundary
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123 nodes of an elements set are also fixed. Any other nodes may be additionally
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126 <li class=kadov-p><p><span style="font-weight: bold;"><B>Smoothing
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127 method</B></span>:</p></li>
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129 <ul type="disc" class="whs5">
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131 <li class=kadov-p><p><span style="font-weight: bold;"><B>Laplacian</B></span>
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132 smoothing pulls a node toward the center of surrounding nodes directly
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133 connected to that node along an element edge. Centroidal smoothing pulls
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134 a node toward the element-area-weighted centroid of the surrounding elements.
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135 Typically, the Laplacian method will produce the mesh with the least element
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136 distortion. It is also the faster method. </p></li>
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138 <li class=kadov-p><p><span style="font-weight: bold;"><B>Centroidal</B></span>
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139 smoothing usually produces a mesh that has more uniform element sizes.
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140 Both methods produce good results with "free" meshes.</p></li>
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147 <p class="whs8"><img src="../image83.gif" width="527px" height="281px" border="0" class="img_whs9"></p>
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149 <ul type="disc" class="whs5">
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151 <li class=kadov-p><p class="whs6"><span
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152 style="font-weight: bold;"><B>Iteration limit: </B></span>both of the smoothing
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153 methods use an iterative procedure to converge toward a smoothed mesh.
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154 All nodes are smoothed according to one of the techniques shown above.
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155 Then the smoothing is reevaluated with the updated nodal locations. This
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156 process continues until the maximum number of iterations has been exceeded,
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157 or all elements has aspect ratio less or equal than the specified one.</p></li>
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159 <li class=kadov-p><p class="whs6"><span
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160 style="font-weight: bold;"><B>Max. aspect ratio</B></span>.</p></li>
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163 <p class="whs2"> </p>
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165 <p class="whs2">3. Click the <span style="font-weight: bold;"><B>Apply
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166 </B></span>or <span style="font-weight: bold;"><B>OK </B></span>button to confirm
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169 <p class="whs2"> </p>
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171 <p class="whs2"><img src="../pics/smoothing1.png" x-maintain-ratio="TRUE" width="353px" height="235px" border="0" class="img_whs10"> <img src="../pics/smoothing2.png" x-maintain-ratio="TRUE" width="351px" height="235px" border="0" class="img_whs11"></p>
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175 <p> <span style="font-weight: bold;"><B>See
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176 Also</B></span> a sample TUI Script of a <a href="../modifying_meshes.htm#bookmark8">Smoothing</a>
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177 operation. </p>
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