Uniform tiling of a circle - Grasshopper2024-03-29T07:48:41Zhttps://www.grasshopper3d.com/forum/topics/uniform-tiling-of-a-circle?groupUrl=kangaroo&commentId=2985220%3AComment%3A1350023&groupId=2985220%3AGroup%3A120977&feed=yes&xn_auth=noFrom a regularized grid you c…tag:www.grasshopper3d.com,2015-08-27:2985220:Comment:13499932015-08-27T17:48:21.436Ztazhttps://www.grasshopper3d.com/profile/taz
<p>From a regularized grid you can see the deformation required to conform to a circle. Below is a K2 setup but the results are similar to what enrique has already produced...</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769034388?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2769034388?profile=RESIZE_1024x1024" width="721" class="align-full"/></a></p>
<p>From a regularized grid you can see the deformation required to conform to a circle. Below is a K2 setup but the results are similar to what enrique has already produced...</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769034388?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2769034388?profile=RESIZE_1024x1024" width="721" class="align-full"/></a></p> Here's some more of my own at…tag:www.grasshopper3d.com,2015-08-27:2985220:Comment:13500322015-08-27T15:22:38.892ZDuncan Whttps://www.grasshopper3d.com/profile/DuncanW
<p>Here's some more of my own attempts that I hope will make clear what I'm after.…</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769034036?profile=original" target="_self"><img class="align-center" src="http://storage.ning.com/topology/rest/1.0/file/get/2769034036?profile=RESIZE_1024x1024" width="721"></img></a></p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769034794?profile=original" target="_self"><img class="align-center" src="http://storage.ning.com/topology/rest/1.0/file/get/2769034794?profile=RESIZE_1024x1024" width="721"></img></a></p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769034974?profile=original" target="_self"><img class="align-center" src="http://storage.ning.com/topology/rest/1.0/file/get/2769034974?profile=RESIZE_1024x1024" width="721"></img></a></p>
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<p>Here's some more of my own attempts that I hope will make clear what I'm after.</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769034036?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2769034036?profile=RESIZE_1024x1024" width="721" class="align-center"/></a></p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769034794?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2769034794?profile=RESIZE_1024x1024" width="721" class="align-center"/></a></p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769034974?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2769034974?profile=RESIZE_1024x1024" width="721" class="align-center"/></a></p>
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<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769035180?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2769035180?profile=RESIZE_1024x1024" width="721" class="align-center"/></a></p>
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<p>All of these have a 'hole' in the middle which I don't want, and the edge lengths are too different.</p>
<p>You can also see the anchor points I had to give. Using just a boundary curve doesn't work and the mesh is sucked up immediately. Why is that?</p>
<p>Ideally, I would not want to use anchor points. I want Kangaroo to choose their position and number for me. How?</p> It's not clear what you're tr…tag:www.grasshopper3d.com,2015-08-27:2985220:Comment:13499542015-08-27T15:04:43.554Ztazhttps://www.grasshopper3d.com/profile/taz
<p>It's not clear what you're trying to accomplish. It sounds like you are looking for a periodic tiling that can be perfectly inscribe in a circle? Mathematically I don't think this is possible with a single triangular tiling.</p>
<p>See <a href="https://en.wikipedia.org/wiki/Euclidean_tilings_of_convex_regular_polygons#Tilings_that_are_not_edge-to-edge" target="_blank">Euclidean tilings of convex regular polygons</a>.</p>
<p>You can create a repeating pattern and test for inclusion within a…</p>
<p>It's not clear what you're trying to accomplish. It sounds like you are looking for a periodic tiling that can be perfectly inscribe in a circle? Mathematically I don't think this is possible with a single triangular tiling.</p>
<p>See <a href="https://en.wikipedia.org/wiki/Euclidean_tilings_of_convex_regular_polygons#Tilings_that_are_not_edge-to-edge" target="_blank">Euclidean tilings of convex regular polygons</a>.</p>
<p>You can create a repeating pattern and test for inclusion within a region...</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769032522?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2769032522?profile=RESIZE_1024x1024" width="721" class="align-full"/></a></p> Many thanks.
Results tend to…tag:www.grasshopper3d.com,2015-08-27:2985220:Comment:13497662015-08-27T14:34:03.956ZDuncan Whttps://www.grasshopper3d.com/profile/DuncanW
<p>Many thanks.</p>
<p>Results tend to be extremly hexagonal looking. To remedy, I've been trying to do this not on a disc but on a fifth or third pizza slice, and then array polarly. Not too successful.</p>
<p>Do I HAVE to use anchor points? Why can't I just tell Kangaroo to use only the circle to pull to, and increase faces dynamically depending on the edge length slider I give it?</p>
<p>Many thanks.</p>
<p>Results tend to be extremly hexagonal looking. To remedy, I've been trying to do this not on a disc but on a fifth or third pizza slice, and then array polarly. Not too successful.</p>
<p>Do I HAVE to use anchor points? Why can't I just tell Kangaroo to use only the circle to pull to, and increase faces dynamically depending on the edge length slider I give it?</p> the filetag:www.grasshopper3d.com,2015-08-27:2985220:Comment:13500232015-08-27T14:04:49.461Zenrique sorianohttps://www.grasshopper3d.com/profile/enriquesoriano
<p>the file</p>
<p>the file</p> Hi Duncan
small mesh but corr…tag:www.grasshopper3d.com,2015-08-27:2985220:Comment:13500192015-08-27T14:02:24.038Zenrique sorianohttps://www.grasshopper3d.com/profile/enriquesoriano
<p>Hi Duncan</p>
<p>small mesh but correct topology> subdivide>pull naked vertices to circle </p>
<p>Then you can play whether you want 7-valence vertices or not, and where do you want them.</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769033954?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2769033954?profile=RESIZE_1024x1024" width="721" class="align-full"/></a></p>
<p>Hi Duncan</p>
<p>small mesh but correct topology> subdivide>pull naked vertices to circle </p>
<p>Then you can play whether you want 7-valence vertices or not, and where do you want them.</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2769033954?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2769033954?profile=RESIZE_1024x1024" width="721" class="align-full"/></a></p>