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94 <h1>Warping</h1>
95
96 <p><img src="../i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> <span style="font-weight: bold;"><B>Warping</B></span> indicates 
97  that a face is not planar and is applied only to 2D elements with 4 nodes. 
98  This quality control criterion is based on a projection plane created 
99  by:</p>
100
101 <p class="whs2">1. bisecting the four element edges, </p>
102
103 <p class="whs2">2. creating a point on the plane at the vector 
104  average of the corners, where the x-axis extends from the point to the 
105  bisector on edge 2. </p>
106
107 <p class="whs3">The plane normal is in the direction of the 
108  cross product of the x-axis and the vector from the origin to the bisector 
109  of edge 3. Every corner of the quad will then be a distance \93h\94 from the 
110  plane. The length of each half edge is measured and the shortest length 
111  is assigned \93l\94. The warp angle is the arcsine of the ratio of the projection 
112  height \93h\94 to the half edge length \93l\94. </p>
113
114 <p>&nbsp;</p>
115
116 <p class="whs2"><img src="../image24.gif" width="496px" height="336px" border="0" class="img_whs4"></p>
117
118 <p class="whs2">&nbsp;</p>
119
120 <p class=TODO>&nbsp;</p>
121
122 <p class=TODO>To apply the Warping quality criterion to your mesh:</p>
123
124 <p class=TODO>&nbsp;</p>
125
126 <p class="whs2">1. Display your mesh in the viewer.</p>
127
128 <p class="whs2">&nbsp;</p>
129
130 <p class="whs2">2. Choose <span style="font-weight: bold;"><B>Controls 
131  &gt; Warp </B></span>or click <img src="../image39.gif" width="23px" height="23px" border="0" class="img_whs5"> button of the toolbar. Your mesh 
132  will be displayed in the viewer with its elements colored according to 
133  the applied mesh quality control criterion:</p>
134
135 <p class="whs2">&nbsp;</p>
136
137 <p class="whs2"><img src="../image97.jpg" width="405px" height="308px" border="0" class="img_whs6"></p>
138
139 <p class="whs2">&nbsp;</p>
140
141 <p class="whs3"><span style="font-weight: bold;"><B>See Also</B></span> 
142  a sample TUI Script of a <a href="../quality_controls.htm#bookmark10">Warping 
143  quality control</a> operation. &nbsp;</p>
144
145 <p>&nbsp;</p>
146
147 <p class="whs2">&nbsp;</p>
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