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109 <h1>Pattern mapping</h1>
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111 <h3>About patterns</h3>
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113 <p><img src="i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> The pattern describes a mesh to generate: positions of
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114 nodes within a geometrical domain and nodal connectivity of elements.
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115 As well, a pattern specifies the so-called key-points, i.e. nodes that
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116 will be located at geometrical vertices. Pattern description is stored
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117 in <pattern_name>.smp file.</p>
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121 <p>The smp file contains 4 sections:</p>
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125 <p class="whs2">1. The first line holds the number of nodes
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128 <p class="whs2"> </p>
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130 <p class="whs2">2. The next N lines describe nodes coordinates.
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131 Each line holds 2 coordinates of a node.</p>
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133 <p class="whs2"> </p>
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135 <p class="whs2">3. A key-points line: indices of nodes to
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136 be mapped on geometrical vertices. An index n refers to a node described
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137 on an n-th line of section 2. The first node index is zero.</p>
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139 <p class="whs2"> </p>
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141 <p class="whs2">4. The rest lines describe nodal connectivity
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142 of elements, one line for an element. A line holds indices of nodes forming
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143 an element. An index n refers to a node described on an n-th line of the
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144 section 2. The first node index is zero. There must be 3 or 4 indices
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145 on a line: only 2d elements are allowed.</p>
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147 <p class="whs2"> </p>
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149 <p>The 2D pattern must contain at least one element and at least one key-point.
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150 All key-points must lay on boundaries.</p>
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154 <p>An example of a simple smp file and a preview of a pattern described
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159 <p><img src="image94.gif" width="626px" height="471px" border="0" class="img_whs3"></p>
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165 <h3>Application of pattern mapping</h3>
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167 <p class=TODO>To apply pattern mapping to a geometrical object:</p>
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169 <p class=TODO> </p>
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171 <p class="whs2">1. From the <span style="font-weight: bold;"><B>Modification
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172 </B></span>menu choose the <span style="font-weight: bold;"><B>Pattern Mapping
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173 </B></span>item or click <img src="image98.gif" width="22px" height="28px" border="0" class="img_whs4"> button in the toolbar. The following
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174 dialog box shall appear:</p>
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176 <p class="whs2"> </p>
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178 <table x-use-null-cells cellspacing="0" width="64.066%" class="whs5">
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182 <tr valign="top" class="whs8">
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183 <td width="56.089%" class="whs9">
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184 <p class="whs10"><img src="pics/patternmapping1.png" x-maintain-ratio="TRUE" width="306px" height="632px" border="0" class="img_whs11"></td>
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185 <td width="43.911%" class="whs12">
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186 <p><img src="pics/patternmapping2.png" x-maintain-ratio="TRUE" width="306px" height="670px" border="0" class="img_whs13"></td></tr>
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189 <p class="whs2"> </p>
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191 <p>To apply a pattern to a geometrical object, you should specify:</p>
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193 <p class="whs2">- a face having the number of vertices equal
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194 to the number of key-points in the pattern; the number of key-points on
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195 internal boundaries of a pattern must also be equal to the number of vertices
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196 on internal boundaries of a face;</p>
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198 <p class="whs2">- a vertex to which the first key-point should
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201 <p class="whs2">- reverse or not the order of key-points.
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202 (The order of vertices of a face is counterclockwise looking from outside).</p>
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206 <p>Then you either load a .smp pattern file previously created manually
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207 by clicking on the <img src="image108.gif" width="34px" height="34px" border="0" class="img_whs14"> button, or click on the <span style="font-weight: bold;"><B>New</B></span>
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208 button for automatic generation.</p>
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210 <p>For an automatic generation you just specify a geometrical face having
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211 a mesh built on it. Mesh nodes lying on face vertices become key-points.
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212 Additionally, you may choose the way of getting nodes coordinates by <span
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213 style="font-weight: bold;"><B>projecting nodes on the face</B></span> instead
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214 of using "positions on face" generated by mesher (if there is
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215 any). Faces having a seam edge can
\92t be used for automatic pattern creation.</p>
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219 <p>When creating a pattern from an existing mesh, there are two possible
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224 <p>1. A sub-mesh on face is selected. A pattern is created from the 2d
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225 elements bound to a face by mesher. Node coordinates are either "positions
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226 on face" computed by mesher, or coordinates got by node projection
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227 on a geometrical surface, according to your choice.</p>
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229 <p>2. A mesh where the main shape is a face, is selected. A pattern is
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230 created from all the 2d elements in a mesh. If all mesh elements are build
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231 by mesher, the user can select the way of getting nodes coordinates, else
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232 all nodes are projected on a face surface.</p>
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234 <table x-use-null-cells cellspacing="0" width="68.686%" class="whs15">
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235 <col class="whs16">
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236 <col class="whs17">
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238 <tr valign="top" class="whs8">
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239 <td width="50.224%" class="whs18">
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240 <p><img src="pics/a-patterntype.png" x-maintain-ratio="TRUE" width="306px" height="428px" border="0" class="img_whs19"></td>
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241 <td width="49.776%" class="whs20">
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242 <p><img src="pics/a-patterntype1.png" x-maintain-ratio="TRUE" width="306px" height="248px" border="0" class="img_whs21"></td></tr>
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247 <h3>Mapping algorithm:</h3>
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249 <p class="whs22">The mapping algorithm is as follows:</p>
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251 <p class="whs22"> </p>
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253 <p class="whs2">1. Key-points are set in the order that they
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254 are encountered when walking along a pattern boundary so that elements
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255 are on the left. The first key-point is preserved.</p>
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257 <p class="whs2">2. Find geometrical vertices corresponding
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258 to key-points by vertices order in a face boundary; here, "Reverse
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259 order of key-points" flag is taken into account.</p>
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261 <p class="whs2"> </p>
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263 <p class="whs2"><img src="image95.gif" width="554px" height="279px" border="0" class="img_whs23"></p>
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265 <p class="whs2"> </p>
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267 <p class="whs2">3. Boundary nodes of a pattern are mapped
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268 onto edges of a face: a node located between certain key-points on a pattern
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269 boundary is mapped on a geometrical edge limited by corresponding geometrical
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270 vertices. Node position on an edge reflects its distance from two key-points.</p>
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272 <p class="whs2"> </p>
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274 <p class="whs2"><img src="image96.gif" width="572px" height="233px" border="0" class="img_whs24"></p>
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276 <p class="whs2"> </p>
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278 <p class="whs2">4. Coordinates of a non-boundary node in
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279 a parametric space of a face are defined as following. In a parametric
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280 space of a pattern, a node lays at the intersection of two iso-lines,
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281 each of which intersects a pattern boundary at least at two points. Knowing
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282 mapped positions of boundary nodes, we find where isoline-boundary intersection
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283 points are mapped to, and hence we can find mapped isolines direction
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284 and then, two node positions on two mapped isolines. The eventual mapped
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285 position of a node is found as an average of positions on mapped isolines.</p>
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287 <p class="whs2"> </p>
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289 <p class="whs2"><img src="image97.gif" width="606px" height="249px" border="0" class="img_whs25"></p>
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291 <p class="whs2"> </p>
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293 <p> <span style="font-weight: bold;"><B>See
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294 Also</B></span> a sample TUI Script of a <a href="modifying_meshes.htm#bookmark13">Pattern
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295 Mapping</a><a href="modifying_meshes.htm#bookmark11"> </a>operation. </p>
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