looking for WEIGHTED voronoi - Grasshopper2024-03-28T13:38:37Zhttps://www.grasshopper3d.com/forum/topics/looking-for-weighted-voronoi?commentId=2985220%3AComment%3A49796&feed=yes&xn_auth=noI have been toying with this…tag:www.grasshopper3d.com,2016-04-05:2985220:Comment:15011512016-04-05T04:44:20.422ZStephen Yoshidahttps://www.grasshopper3d.com/profile/StephenYoshida
<p>I have been toying with this lately and have run into some issues. Namely the intersection command no longer calculates intersections for all combinations of breps.</p>
<p></p>
<p>I found two solutions to this:</p>
<ol>
<li><a href="http://www.grasshopper3d.com/forum/topics/brep-intersections" target="_blank">A visual basic script c/o DR found here</a></li>
<li>A boolean union of all the cones with a simple project onto surface. </li>
</ol>
<p></p>
<p>This shouldn't have taken me a day to…</p>
<p>I have been toying with this lately and have run into some issues. Namely the intersection command no longer calculates intersections for all combinations of breps.</p>
<p></p>
<p>I found two solutions to this:</p>
<ol>
<li><a href="http://www.grasshopper3d.com/forum/topics/brep-intersections" target="_blank">A visual basic script c/o DR found here</a></li>
<li>A boolean union of all the cones with a simple project onto surface. </li>
</ol>
<p></p>
<p>This shouldn't have taken me a day to work through given how stupid the solution was so hopefully it will work better for you reading this in the future.</p> Matt,
The AW-Voronoi diagra…tag:www.grasshopper3d.com,2011-02-02:2985220:Comment:1554942011-02-02T18:55:26.807ZJacek Jaskólskihttps://www.grasshopper3d.com/profile/JacekJaskolski
<p>Matt,</p>
<p> </p>
<p>The AW-Voronoi diagramm is "scale-aware" so the reason for the jagged output lines is probably that the weights are set too high in relation to the distances of the points.</p>
<p> </p>
<p>See this example:</p>
<p>1. When the weights are too large, the circles intersect, and the diagram is corrupt:</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768635520?profile=original" target="_self"><img class="align-full" src="http://storage.ning.com/topology/rest/1.0/file/get/2768635520?profile=RESIZE_1024x1024" width="600"></img></a> (to see the circles enable preview on the circle…</p>
<p>Matt,</p>
<p> </p>
<p>The AW-Voronoi diagramm is "scale-aware" so the reason for the jagged output lines is probably that the weights are set too high in relation to the distances of the points.</p>
<p> </p>
<p>See this example:</p>
<p>1. When the weights are too large, the circles intersect, and the diagram is corrupt:</p>
<p><a target="_self" href="http://storage.ning.com/topology/rest/1.0/file/get/2768635520?profile=original"><img class="align-full" width="600" src="http://storage.ning.com/topology/rest/1.0/file/get/2768635520?profile=RESIZE_1024x1024"/></a>(to see the circles enable preview on the circle component)</p>
<p>(to manipulate with the scale insert a multiply component and a slider, as shown above)</p>
<p> </p>
<p>2. If you adjust the weights so that they don't intersect, you'll get a reasonable result:</p>
<p><a target="_self" href="http://storage.ning.com/topology/rest/1.0/file/get/2768635907?profile=original"><img class="align-full" width="600" src="http://storage.ning.com/topology/rest/1.0/file/get/2768635907?profile=RESIZE_1024x1024"/></a></p>
<p>3. To enhance the solution, lower the "precision factor" (here set from 1.0 to 0.25) which controls the number of divisions of the circles:</p>
<p><a target="_self" href="http://storage.ning.com/topology/rest/1.0/file/get/2768636113?profile=original"><img class="align-full" width="600" src="http://storage.ning.com/topology/rest/1.0/file/get/2768636113?profile=RESIZE_1024x1024"/></a></p>
<p> </p>
<p>Keep in mind that the definition is just a sketch, a proof of concept rather...</p>
<p>JJ</p> Jacek,
This looks very nice a…tag:www.grasshopper3d.com,2011-02-01:2985220:Comment:1552512011-02-01T23:13:14.664ZMatthttps://www.grasshopper3d.com/profile/MatthewCrowley
<p>Jacek,</p>
<p>This looks very nice and direct. When I am using your definition I get jagged lines and the approximation misses at times. Is there a way to tweak the definition to get results like what you have posted?</p>
<p>Jacek,</p>
<p>This looks very nice and direct. When I am using your definition I get jagged lines and the approximation misses at times. Is there a way to tweak the definition to get results like what you have posted?</p> Ok I managed to solved this t…tag:www.grasshopper3d.com,2010-11-25:2985220:Comment:1363442010-11-25T15:06:47.915ZJesus Galvezhttps://www.grasshopper3d.com/profile/JesusGalvez
Ok I managed to solved this thanx to <a href="http://www.grasshopper3d.com/forum/topics/is-it-possible-to-trim-or">Jeff Niemasz VB</a>.
Ok I managed to solved this thanx to <a href="http://www.grasshopper3d.com/forum/topics/is-it-possible-to-trim-or">Jeff Niemasz VB</a>. Is it possible to have the re…tag:www.grasshopper3d.com,2010-11-25:2985220:Comment:1362462010-11-25T07:51:34.557ZJesus Galvezhttps://www.grasshopper3d.com/profile/JesusGalvez
Is it possible to have the resulting curves made into surfaces and then extruded?
Is it possible to have the resulting curves made into surfaces and then extruded? very nice aproximation!tag:www.grasshopper3d.com,2010-05-13:2985220:Comment:651792010-05-13T23:17:45.042Zenrique sorianohttps://www.grasshopper3d.com/profile/enriquesoriano
very nice aproximation!
very nice aproximation! Cones are the most awesome ty…tag:www.grasshopper3d.com,2010-04-17:2985220:Comment:599772010-04-17T14:47:22.771ZDavid Ruttenhttps://www.grasshopper3d.com/profile/DavidRutten
Cones are the most awesome type of geometry on this green Earth.<br />
<br />
--<br />
David Rutten<br />
david@mcneel.com<br />
Poprad, Slovakia
Cones are the most awesome type of geometry on this green Earth.<br />
<br />
--<br />
David Rutten<br />
david@mcneel.com<br />
Poprad, Slovakia thanks to Jacek Jaskólsk for…tag:www.grasshopper3d.com,2010-04-17:2985220:Comment:599712010-04-17T14:32:43.807ZAndrei Raducanuhttps://www.grasshopper3d.com/profile/AndreiRaducanu
thanks to Jacek Jaskólsk for the great input!
thanks to Jacek Jaskólsk for the great input! There's a quick way to approx…tag:www.grasshopper3d.com,2010-04-17:2985220:Comment:599702010-04-17T14:12:11.945ZJacek Jaskólskihttps://www.grasshopper3d.com/profile/JacekJaskolski
There's a quick way to approximate additively weighted Voronoi diagrams:<br />
- draw circles positioned at the generator points, with radii sizes corresponding to point weights<br />
- sample (divide) the circles<br />
- create an ordinary Voronoi diagram using the division points as generator points<br />
- merge cells around base generator points<br />
<br />
It's a very simple and fast method which came to my mind after reading…
There's a quick way to approximate additively weighted Voronoi diagrams:<br />
- draw circles positioned at the generator points, with radii sizes corresponding to point weights<br />
- sample (divide) the circles<br />
- create an ordinary Voronoi diagram using the division points as generator points<br />
- merge cells around base generator points<br />
<br />
It's a very simple and fast method which came to my mind after reading <a href="http://www.whitman.edu/mathematics/SeniorProjectArchive/2005/dobrinat.pdf" target="_blank">Adam Dobrin's paper</a>. I've attached a simple definition - works fine as long as generator points do not dominate each other:<br />
<p style="text-align: left;"><a class="noborder" href="http://storage.ning.com/topology/rest/1.0/file/get/2768604993?profile=original" target="_blank"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768604993?profile=RESIZE_1024x1024" alt=""/></a></p> I don't understand how inters…tag:www.grasshopper3d.com,2010-04-17:2985220:Comment:599592010-04-17T12:07:57.482ZJacek Jaskólskihttps://www.grasshopper3d.com/profile/JacekJaskolski
I don't understand how intersecting spheres should give you the proper solution...<br />
<br />
Daniel's idea is the one if your'e looking for a simple (though painfully slow) definition.<br />
<br />
What's more, there are various types of weighted Voronoi diagrams. Among others there are the <i>multiplicatively weighted</i> and the <i>additively weigthed</i> diagram concepts. There's a good short review by Adam Dobrin <a href="http://www.whitman.edu/mathematics/SeniorProjectArchive/2005/" target="_blank">here</a>,…
I don't understand how intersecting spheres should give you the proper solution...<br />
<br />
Daniel's idea is the one if your'e looking for a simple (though painfully slow) definition.<br />
<br />
What's more, there are various types of weighted Voronoi diagrams. Among others there are the <i>multiplicatively weighted</i> and the <i>additively weigthed</i> diagram concepts. There's a good short review by Adam Dobrin <a href="http://www.whitman.edu/mathematics/SeniorProjectArchive/2005/" target="_blank">here</a>, which covers the definitions, as well as some of the properties and uses of different variations of the Voronoi diagram.<br />
<br />
Interestingly, the <i>intersecting cones method</i> can be used to draw both MW and AW diagrams:<br />
<br />
MW - cones with different base radius, same height:<br />
<p style="text-align: left;"><a class="noborder" href="http://storage.ning.com/topology/rest/1.0/file/get/2768605102?profile=original" target="_blank"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768605102?profile=RESIZE_1024x1024" alt=""/></a></p>
<br />
AW - cones scaled accordingly to assigned weights:<br />
<p style="text-align: left;"><a class="noborder" href="http://storage.ning.com/topology/rest/1.0/file/get/2768605391?profile=original" target="_blank"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768605391?profile=RESIZE_1024x1024" alt=""/></a></p>