May 25th, 2012 - Medial Axis - Grasshopper2024-03-29T02:28:45Zhttps://www.grasshopper3d.com/forum/topics/may-25th-2012-medial-axis?groupUrl=coffee-and-grasshopper&commentId=2985220%3AComment%3A606068&groupId=2985220%3AGroup%3A560791&feed=yes&xn_auth=nohello! is there any way to ob…tag:www.grasshopper3d.com,2016-10-20:2985220:Comment:16221952016-10-20T20:56:12.878Zrebeccahttps://www.grasshopper3d.com/profile/rebecca817
<p>hello! is there any way to obtain a medial axis w/in a 3D volume like this?</p>
<p>I am trying to extract the interior volume as an object instead of the negative of a Boolean operation.</p>
<p>I'm hoping to get a media axis between surfaces within this volume to then pipe/t-spline into a new object.</p>
<p>hello! is there any way to obtain a medial axis w/in a 3D volume like this?</p>
<p>I am trying to extract the interior volume as an object instead of the negative of a Boolean operation.</p>
<p>I'm hoping to get a media axis between surfaces within this volume to then pipe/t-spline into a new object.</p> Hi Luis,
I created this geome…tag:www.grasshopper3d.com,2016-02-27:2985220:Comment:14726112016-02-27T01:37:16.157Zrebeccahttps://www.grasshopper3d.com/profile/rebecca817
<p>Hi Luis,</p>
<p>I created this geometry via tspline tweaks on Rhino.</p>
<p>In order to have more control over the generative form, I was looking up ways to work with tsplines in grasshopper and found threads on voronoi medial axes.</p>
<p>I ran your definition and wondering how best to apply tsplines to the resulting voronoi curves? Or is this even the best way?</p>
<p>Many thanks again - your definition was very helpful.</p>
<p>RP</p>
<p>Hi Luis,</p>
<p>I created this geometry via tspline tweaks on Rhino.</p>
<p>In order to have more control over the generative form, I was looking up ways to work with tsplines in grasshopper and found threads on voronoi medial axes.</p>
<p>I ran your definition and wondering how best to apply tsplines to the resulting voronoi curves? Or is this even the best way?</p>
<p>Many thanks again - your definition was very helpful.</p>
<p>RP</p> Hello,
Very interesting analy…tag:www.grasshopper3d.com,2013-03-22:2985220:Comment:8157152013-03-22T13:58:55.324ZChristos Antonopouloshttps://www.grasshopper3d.com/profile/CHRISTOSANTONOPOULOS
<p>Hello,</p>
<p>Very interesting analysis.</p>
<p>I have started a discussion here </p>
<p><a href="http://www.grasshopper3d.com/forum/topics/skeleton-frame-of-a-given-mesh" target="_blank">http://www.grasshopper3d.com/forum/topics/skeleton-frame-of-a-given-mesh</a></p>
<p>essentially looking for the same principle applied in a 3d mesh.</p>
<p></p>
<p>Any idea very much appreciated.</p>
<p></p>
<p>Thank you,</p>
<p>Christos</p>
<p>Hello,</p>
<p>Very interesting analysis.</p>
<p>I have started a discussion here </p>
<p><a href="http://www.grasshopper3d.com/forum/topics/skeleton-frame-of-a-given-mesh" target="_blank">http://www.grasshopper3d.com/forum/topics/skeleton-frame-of-a-given-mesh</a></p>
<p>essentially looking for the same principle applied in a 3d mesh.</p>
<p></p>
<p>Any idea very much appreciated.</p>
<p></p>
<p>Thank you,</p>
<p>Christos</p> Yes, I see your point. I thi…tag:www.grasshopper3d.com,2012-05-27:2985220:Comment:6059982012-05-27T12:59:13.330ZLuis Fraguadahttps://www.grasshopper3d.com/profile/LuisFraguada
<p>Yes, I see your point. I think you are also right about the center point / end points relationship not necessarily being the closest points...</p>
<p>if we keep going, eventually we will get it ;)</p>
<p>Yes, I see your point. I think you are also right about the center point / end points relationship not necessarily being the closest points...</p>
<p>if we keep going, eventually we will get it ;)</p> Because they are the midpoint…tag:www.grasshopper3d.com,2012-05-27:2985220:Comment:6060692012-05-27T12:25:37.974ZAdam Hollowayhttps://www.grasshopper3d.com/profile/AdamHolloway
<p>Because they are the midpoint of the lines from the delaunay diagram they are equidistant from exactly two points on the perimeter, but i guess they aren't always necessarily the nearest points, so maybe its still an approximation:</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768731108?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768731108?profile=RESIZE_1024x1024" width="721" class="align-full"/></a></p>
<p>Because they are the midpoint of the lines from the delaunay diagram they are equidistant from exactly two points on the perimeter, but i guess they aren't always necessarily the nearest points, so maybe its still an approximation:</p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768731108?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768731108?profile=RESIZE_1024x1024" width="721" class="align-full"/></a></p> Why is it more accurate? Aga…tag:www.grasshopper3d.com,2012-05-27:2985220:Comment:6060682012-05-27T12:09:32.058ZLuis Fraguadahttps://www.grasshopper3d.com/profile/LuisFraguada
<p>Why is it more accurate? Again, take a look at where those points go when you use a CurveCP component. Using the distance as a radius for a circle, it still does not meet the bounding curve at more than one location...</p>
<p>Why is it more accurate? Again, take a look at where those points go when you use a CurveCP component. Using the distance as a radius for a circle, it still does not meet the bounding curve at more than one location...</p> This method, using a delaunay…tag:www.grasshopper3d.com,2012-05-26:2985220:Comment:6058442012-05-26T18:05:13.809ZAdam Hollowayhttps://www.grasshopper3d.com/profile/AdamHolloway
<p>This method, using a delaunay connectivity diagram, appears more accurate (in theory) and uses less components, but I don't get a curve as a result:…<a href="http://storage.ning.com/topology/rest/1.0/file/get/2768731643?profile=original" target="_self"><img class="align-full" src="http://storage.ning.com/topology/rest/1.0/file/get/2768731643?profile=RESIZE_1024x1024" width="721"></img></a></p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768731818?profile=original" target="_self"><img class="align-left" src="http://storage.ning.com/topology/rest/1.0/file/get/2768731818?profile=RESIZE_1024x1024" width="721"></img></a></p>
<p>This method, using a delaunay connectivity diagram, appears more accurate (in theory) and uses less components, but I don't get a curve as a result:<a href="http://storage.ning.com/topology/rest/1.0/file/get/2768731643?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768731643?profile=RESIZE_1024x1024" width="721" class="align-full"/></a></p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768731818?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768731818?profile=RESIZE_1024x1024" width="721" class="align-left"/></a></p> Well, the solution I got was…tag:www.grasshopper3d.com,2012-05-26:2985220:Comment:6054882012-05-26T11:16:11.596ZAdam Hollowayhttps://www.grasshopper3d.com/profile/AdamHolloway
<p>Well, the solution I got was the same as you Luis (using voronoi), although you did it in less components than me:</p>
<p></p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768732993?profile=original" target="_self"><img class="align-left" src="http://storage.ning.com/topology/rest/1.0/file/get/2768732993?profile=RESIZE_1024x1024" width="721"></img></a></p>
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<p><br></br><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768733111?profile=original" target="_self"><img class="align-left" src="http://storage.ning.com/topology/rest/1.0/file/get/2768733111?profile=RESIZE_1024x1024" width="721"></img></a> It seems though that you have proved that it isn't exactly the medial axis…</p>
<p>Well, the solution I got was the same as you Luis (using voronoi), although you did it in less components than me:</p>
<p></p>
<p><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768732993?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768732993?profile=RESIZE_1024x1024" width="721" class="align-left"/></a></p>
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<p><br/><a href="http://storage.ning.com/topology/rest/1.0/file/get/2768733111?profile=original" target="_self"><img width="721" src="http://storage.ning.com/topology/rest/1.0/file/get/2768733111?profile=RESIZE_1024x1024" width="721" class="align-left"/></a>It seems though that you have proved that it isn't exactly the medial axis that we are getting, so I guess no one has really succeeded... </p>
<p></p>
<p>I did think though that maybe there is another simple way of doing it, based on the article I posted, by generating circles from sets of 3 points on the curve that have normal vectors at obtuse angles to each other. I am looking into figuring this out now. </p> 5. The poster judges the answ…tag:www.grasshopper3d.com,2012-05-26:2985220:Comment:6057172012-05-26T07:56:41.919ZLuis Fraguadahttps://www.grasshopper3d.com/profile/LuisFraguada
<blockquote><p>5. The poster judges the answer. They should offer a sample solution as well when they declare the winner.</p>
<p></p>
</blockquote>
<p>I am looking forward to the sample solution from Adam...</p>
<p></p>
<blockquote><p>5. The poster judges the answer. They should offer a sample solution as well when they declare the winner.</p>
<p></p>
</blockquote>
<p>I am looking forward to the sample solution from Adam...</p>
<p></p> I bet this is how GCode for V…tag:www.grasshopper3d.com,2012-05-25:2985220:Comment:6052102012-05-25T19:26:59.165ZMateusz Zwierzyckihttps://www.grasshopper3d.com/profile/MateuszZwierzycki
<p>I bet this is how GCode for V carving is made. Do you know about any papers that show how to make exact medial axis ? Wikipedia says that curves of medial axis are parabolic, so should be possible to do that.</p>
<p></p>
<p>Back to GCode : distance to closest point on curve = Z axis movement.</p>
<p>I bet this is how GCode for V carving is made. Do you know about any papers that show how to make exact medial axis ? Wikipedia says that curves of medial axis are parabolic, so should be possible to do that.</p>
<p></p>
<p>Back to GCode : distance to closest point on curve = Z axis movement.</p>