Online since 2002. Over 3300 puzzles, 2600 worldwide members, and 270,000 messages.

TwistyPuzzles.com Forum
 It is currently Wed Jul 23, 2014 10:01 pm

 All times are UTC - 5 hours

 Page 1 of 1 [ 2 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: A question about closest points and geometryPosted: Thu Mar 20, 2014 12:59 am

Joined: Sat Apr 21, 2007 11:21 pm
Location: Marin, CA
Let's say I have some 3 dimensional space with some number of meshes inside. (Could be puzzle parts for example.)
I know that none of them are closer than 1mm to any other part.
I'm only given the centroid locations as X, Y, Z coordinates, and a list for each part of the other parts that are within <= 1mm of a collision.

I connect each centroid to the centroids around it with an edge. I end up with a new non manifold network of edges and centroids.

Rotations are not allowed for what comes next.

Now, no matter how many centroids I have, it is safe to move any one centroid in any direction by 0.5mm without introducing a collision, right?

If I constrict all the edges by some amount like 0.4 and solve iteratively for the constraint that a centroid can't move locally more than 0.5mm relative to another connected centroid, including the direction the edge originally pointed in, am I still guaranteed a non-colliding system?

Or am I missing something?

If one of you knows a pure linear algebra way to do this I'll be impressed.

_________________
Jason Smith posted here as 'io' through 2012.
Visit Jason Smith's PuzzleForge on Shapeways!
Jason Smith's Puzzles - YouTube Channel.

Top

 Post subject: Re: A question about closest points and geometryPosted: Thu Mar 20, 2014 2:43 am

Joined: Thu Jan 06, 2005 8:53 pm
Location: Los Angeles
I certainly can't think of any counterexample.
However, without taking the shapes into account, you certainly won't be able to get maximum compression.

And I'm guessing you're trying to minimize some property? Bounding box, or empty space perhaps?

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 2 posts ]

 All times are UTC - 5 hours

#### Who is online

Users browsing this forum: No registered users and 7 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ Announcements General Puzzle Topics New Puzzles Puzzle Building and Modding Puzzle Collecting Solving Puzzles Marketplace Non-Twisty Puzzles Site Comments, Suggestions & Questions Content Moderators Off Topic