Difference between revisions of "Reference Talk:Tiling Pattern"

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* Adding a table of unit square normalization scales.
 
  
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[[Category:Patterns]]
 
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{{#indexentry:tiling, keyword}}
 
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{{#indexentry:tiling, pattern}}
 
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{{#indexentry:keyword, tiling}}
 
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{{#indexentry:pattern, tiling}}
 
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<p>The <code>tiling</code> pattern creates a series tiles in the x-z plane. See the image below for examples of the twenty-seven available patterns.</p>
 
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<p>The syntax is as follows:</p>
 
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<pre>
 
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pigment {
 
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  tiling Pattern_Number
 
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  [PATTERN_MODIFIERS...]
 
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  }
 
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</pre>
 
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<table class="centered" width="580px" cellpadding="0" cellspacing="10">
 
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<tr>
 
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  <td>[[Image:RefImgTiling2.gif|center|560px<!--centered--->]]</td>
 
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</tr>
 
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<tr>
 
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  <td><p class="caption">The various tiling patterns annotated by tiling pattern and tiling type respectively</p></td>
 
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</tr>
 
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</table>
 
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<p>For each pattern, each individual tile of the pattern has the same beveling as the other tiles in that pattern, allowing regular caulking to be defined. For a pattern with N tile types (where N is the tiling type noted in the above image) the main color/texture of the tiles are at x/N with x going from 0 to N-1, and the extreme color/texture caulk for these tiles are at (x+1)/N. The bevel covers the range between these two values.</p>
 
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<p>To begin exploring the <code>tiling</code> pattern right away, see the distribution file <code>~scenes/textures/pattern/tiling.pov</code>. It uses obvious colors to better illustrate how the feature works, and you can optionally write it's <code>color_map</code> to a text file. Once you get a feel for the break points, you can always define you own map!</p>
 
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<p>The scale required to fit the core repeated tile into a unit square size for each tiling pattern is given in the table below.</p> 
 
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<table class="centered" cellpadding="5" cellspacing="0" border="5" border-collapse="collapse">
 
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<tr>
 
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  <th>Tiling Number</th>
 
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  <th>Unit square normalization scale</th>
 
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</tr>
 
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<tr><td> 1</td> <td><1,1,1>                                </td></tr>
 
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<tr><td> 2</td> <td><2/3,1,1/sqrt(3)>                      </td></tr>
 
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<tr><td> 3</td> <td><1,1,2/sqrt(3)>                        </td></tr>
 
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<tr><td> 4</td> <td><1,1,2/sqrt(3)>                        </td></tr>
 
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<tr><td> 5</td> <td><2/3,1,1/sqrt(3)>                      </td></tr>
 
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<tr><td> 6</td> <td><1/4,1,1/4>                            </td></tr>
 
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<tr><td> 7</td> <td><1/(sqrt(2)+1),1,1/(sqrt(2)+1)>        </td></tr>
 
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<tr><td> 8</td> <td><1,1,1/(sqrt(3)+2)>                    </td></tr>
 
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<tr><td> 9</td> <td><1/2,1,1/(2*sqrt(3))>                  </td></tr>
 
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<tr><td>10</td> <td><1,1,1/2>                              </td></tr>
 
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<tr><td>11</td> <td><1/3,1,1/3>                            </td></tr>
 
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<tr><td>12</td> <td><1/3,1,1/3>                            </td></tr>
 
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<tr><td>13</td> <td><1/(sqrt(3)+1),1,1/(sqrt(3)+1)>        </td></tr>
 
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<tr><td>14</td> <td><1/(sqrt(3)+1),1,1/(sqrt(3)+1)>        </td></tr>
 
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<tr><td>15</td> <td><1/5,1,1/5>                            </td></tr>
 
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<tr><td>16</td> <td><1/(sqrt(3)+3),1,1/((sqrt(3)+1.0)*2.0)></td></tr>
 
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<tr><td>17</td> <td><1/(sqrt(3)+3),1,1/((sqrt(3)+1.0)*2.0)></td></tr>
 
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<tr><td>18</td> <td><1/4,1,1/4>                            </td></tr>
 
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<tr><td>19</td> <td><1/2,1,1/((sqrt(3)/2)*3)>              </td></tr>
 
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<tr><td>20</td> <td><1/2,1,1/((sqrt(3)/2)*3)>              </td></tr>
 
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<tr><td>21</td> <td><1/(1+sqrt(3)),1,1/(1+sqrt(3))>        </td></tr>
 
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<tr><td>22</td> <td><1/(2+sqrt(3)),1,1/(3+(2*sqrt(3)))>    </td></tr>
 
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<tr><td>23</td> <td><1/(3+sqrt(3)),1,1/(3+(3*sqrt(3)))>    </td></tr>
 
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<tr><td>24</td> <td><1/(3+sqrt(3)),1,1/(3+(3*sqrt(3)))>    </td></tr>
 
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<tr><td>25</td> <td><1/(4*sqrt(2)),1,1/(4*sqrt(2))>  (*)  </td></tr>
 
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<tr><td>26</td> <td><1/(4*sqrt(2)),1,1/(4*sqrt(2))>  (*)  </td></tr>
 
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<tr><td>27</td> <td><1/(4*sqrt(2)),1,1/(4*sqrt(2))>  (*)  </td></tr>
 
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<tr>
 
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  <td colspan="2"><p class="caption">(*) - Unit square scaling not possible with penrose tiling. Scaling given useful to see all tiles in a way symmetrical in z.</p></td>
 
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</tr>
 
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</table>
 

Latest revision as of 14:43, 27 September 2016

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