Wolfram Mathematica

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The Substitute

4:45 AM

off topic. is there a way to plot multiple (overlapping) graphs in WolframAlpha?

nevermind doh

7 hours later…

Szabolcs

12:05 PM

Check this out if you use LibraryLink:

Q: How to simplify writing LibraryLink code?

LibraryLink is an API for extending Mathematica through C or C++. It is very fast because it gives direct access to Mathematica's packed array data structure, without even needing to make a copy of the arrays. Unfortunately, working with LibraryLink involves writing a lot of tedious boilerplate...

Meta

Q: how to paste codes and expressions from mathematica to forum (here)

can anyone tell me how to copy expressions from mathematica and paste them here, without any change. so that you can exactly see what is in my mathematica window... i've trouble asking question here... please help ... tnx

discussion

3 hours later…

halirutan

3:19 PM

Can someone tell me whether I have somehow misunderstood the OP's question here?

A: Problem trying to compile JLink application

Unless you tell us exactly what you typed on the commandline, there is no way of knowing what went wrong. Let me give you a head-start. My Mathematica installation is in the directory /usr/local/Wolfram/Mathematica/10.2 Therefore, to start the SampleProgram I go into the directory where Sam...

No comment, no down-vote, no up-vote, no nothing.

Pickett

@halirutan +1, I think that's right. It's odd that the OP hasn't taken any action since he put a bounty on the question.

halirutan

@Pickett That's what's so confusing. Bounties should attract attention which it did, because I had not notice the question earlier. But the complete silence of the OP is odd.

Pickett

This week's update to PackageData:
- Packages hosted on Github with "releases" now have direct download links on the site. These are retrieved automatically for any Github hosted package.
- Usability improvements
- The RSS feed now only includes new packages, not updates as well.
- Old usage example texts can now be reached from the history page of packages.
- Latex is now rendered in the usage examples editor's live preview.

1 hour later…

Szabolcs

4:35 PM

@nikie I've been playing a lot with different approaches this weekend, and I was planning to implement this in 3D (MATLAB's is only 2D). But the anisotropy still bothers me. The quasi-euclidean method in MATLAB distinguishes between 8 directions, which is much better than 4 (Manhattan distance), but I'm not quite satisfied with it ...

@nikie Do you know of any tricks to make it a bit more isotropic, while preserving the same basic approach?

Maybe I should just simulate something like a wave equation inside of the region ... that is isotropic, but slow. Must ensure no reflections from the walls. Somehow trying to do this seems like not such a good idea though ...

halirutan

@Szabolcs As far as I no, there is not. Your only chance is to use more directions or switch the approach completely.

Szabolcs

4:59 PM

@halirutan I guess I could allow jumping two pixels at a time which would give me 16 directions, and call that good enough.

halirutan

@Szabolcs As far as I remember there is a reference to this on the wiki page. Let me see..

@Szabolcs found something similar. Have you seen this?

Q: True shortest path in binary image/map

How can i find the true shortest path in a binary image/map? I have looked into Different algorithms, e.g. Dijkstra and A* but they only yield an approximateion of the the shortest path as all pixels are only connected in a "8 connected" way. What algorithm can i use to get the true shortest p...

dijkstra shortest-path a-star

Szabolcs

@halirutan Haven't seen that yet! I'll read it later, have to go, have guests ...

halirutan

@Szabolcs Dinner here.. Have fun.

Michael Hale

5:17 PM

@Szabolcs Besides the article on "any-angle shortest paths" there is the one on "Euclidean shortest paths". The basic idea is you are either taking a straight line to the goal, or a straight line to a visible obstacle corner at each step. So you could build a graph of which obstacle corners are visible to each other. Add in your start and end points and what corners are visible to them. Then find the shortest path on that graph. Depends on how much effort is worth it for you.

3 hours later…

Szabolcs

8:01 PM

@MichaelHale Finding those points sounds quite difficult though ... maybe with a suitable discretization (like BoundaryMeshRegion) it will be easier

Another idea I thought of tonight was to find some approximation of the shortest paths with the above methods, then convert the path to a polyline (if it is in pixels), then finally use variational methods to greedily optimize the length of the line

Try to minimize the curvature

Try to do the analog of putting the two ends of a rope in the two points, then pulling it tight

This wouldn't work if the initial path is routed around the wrong obstacle, but if the initial path is at least topologically correct then it will be good

And luckily my actual use case is very weird shaped, but at least singly connected (I think!)

Mesh based, for fun:

Finer mesh:

Michael Hale

@Szabolcs That sounds interesting, but I don't think it's that hard to find the coordinates of the perimeter. Just take every black pixel. Check its 8 neighbors. If the neighbor is white then the corner or corners of the black pixel that it touches are boundary coordinates. You could also dilate by a pixel and do morphological perimeter, then just take the corners of those pixels. The test I did with a region of all of the squares didn't work well though.

So you'd have to write your own line/square intersection test.

Then build the graph of what edge pixels are visible from which other edge pixels.

Or coordinates I mean.

Szabolcs

8:42 PM

There's a freely available book dealing with the topic: cs.smith.edu/~orourke/books/ArtGalleryTheorems

Written by an M.SE user.

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