I need a efficient way the draw some finite automata , I tried using word shapes but it very exhausting. I looking for another way to do that only by mouse drawing (not java extant like jgraph or graphviz).
EDIT :
Since no one answered me , after some tests I think that best way to draw simple automata is using power point .
If you want alternatives for windows the famous one is xfig. There is also IPE. The hardcore automators use gastex.
Related
I'm making a program that implements procedural content generation (PCG) to create maps in a 2d game.
I use the graph data structure as the basis. then the graph will be transformed into a map like in the example image I attached.
with graph specifications as follows:
-vertex can have more than 4 edges
-allowed the formation of cycles in the graph
any suggestions on what method I can use to transform the graph to a 2d map in a grid with space-tight results?
thanks
Uh, that is a tough one. The first problem you will encounter is whether this is even possible for the graph you use. See more below for that specific topic.
Let's say we ignore the fact that your graph could be impossible to map to a grid. I faced the same issue in my Master's Thesis a few years back. (PDF available here; 3.4 World Generation; page 25). I tried to find an algorithm, that could generate my world from a graph structure but ultimately failed. I tried placing one element after the other and implemented some backtracking in case it got stuck. But in the end you're facing a similar complexity to calculating chess moves. At some point you know you messed up, but you don't know how many steps you should go back/reverse, before trying the next one. If you try to solve this by brute force, you're not going to have a good time. And I did not come up with good heuristics to solve it in an adequate time.
My solution: I decided in the end to go with AnswerSet Programming. You're basically not solving the problem with an algorithm, but you find a (more or less) elegant logical representation of your problem and let a logic solver (program specifically made to find a valid solution to your logical problem-representation) do the work. Have a look in my thesis about the details, it was a few years ago and I didn't use one since. I remember however, that this process was not easy and it took me a few days to find a good logical representation of my problem.
Another question to ask: Could you work on the grid directly? Or maybe on a graph structure representing a grid? In the end a grid is nothing else than a graph; every cell is a node and neighbouring connections are the edges. I have quite some experience in the field and would be happy to help you, if you'd like to share what you want to achieve with your generator. I have also a vast collection of resources about procedural generation, maybe you find something helpful there, too.
More on the planarity of a graph: For your graph to be mappable to a plane, it needs to be planar, and checking so is also not trivial. The easiest way - if I'm not mistaken - is to prove the existence of a non-planar sub-graph, e.g. the K5 (the smallest non-planar a complete graph) or K3,3 (the smallest non-planar complete bipartite graph). And even if your graph is planar, it is not necessarily guaranteed that you can put it on your grid.
This has to be a well researched problem, but I am struggling researching it.
I started here, but I am looking for algorithms to study and implement.
http://en.wikipedia.org/wiki/Graph_isomorphism_problem
For example, if I have two of these DAGs (Directe Acyclic Graphs), I want to mark/delete one of them because it is just a rotation/reflection of the first. Being in the same automorphism group means they can be rotated/reflected to have the exact same adjacency matrix right?
you can use nauty or saucy algorithm to compute this problem.
This links might be helpful to you. :)
Nauty:
http://cs.anu.edu.au/~bdm/nauty/
http://cs.anu.edu.au/~bdm/nauty/
Saucy:
http://vlsicad.eecs.umich.edu/BK/SAUCY/
There is also a list of ready made tools available (especially for command line in linux based OS), in the saucy page.
Does someone have an implementation of Iterative Closest Point (ICP) algorithm for two dimensions (2D) in R?
Here is an attempt in c#
Iterative Closest Point Implementation
Here is a more general question
iterative closest point library
This is to match two sets of points through translation and scaling.
Spacedman's comment is probably best. You might also take a look at http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=12627&objectType=file for a matlab implementation. Assuming it works ok, translating Matlab to R code is relatively easy.
This is somewhat of an answer in the form of a non-answer.
There are many variants of ICP. The design choices are at least partially organized by the late 90's Ph.D. work of Pulli and by Rusinkiewicz & Levoy. If you're going to be using ICP for anything remotely important (translation: "more than just a class assignment"), you should understand the tradeoffs.
Thus, it's probably best to take one of the existing implementations and port it to R.
3 Years too late, but there is the function icpmat in the package Morpho by the same guy who wrote Rvcg. I don't know which variant is implemented though.
Link:
https://github.com/zarquon42b/Morpho
There is a self-contained (as far as I can tell) C++ implementation of ICP here. Maybe you can create your own R wrapper around this C++ code.
I've been wondering how programs like mathematica and mathlab, and so on, plot graphs of functions so gracefully and fast. Can anyone explain to me how they do this and, furthermore, how I can do this? Is it related to an aspect or course in Computer Programming or Math? Which then?
Well, with some encouragement from belisarius, here's a my comment as an answer: try looking at matplotlib. From the home page:
matplotlib is a python 2D plotting library which produces publication quality figures in a variety of hardcopy formats and interactive environments across platforms. matplotlib can be used in python scripts, the python and ipython shell (ala MATLAB®* or Mathematica®†), web application servers, and six graphical user interface toolkits.
It was originally inspired by MATLAB's plotting capabilities, though it's grown a lot since then. It's solid software - and it's open source, under a BSD license, so not only can you read the source, you can hack on it and use it in whatever you like.
Another place you could look is gnuplot. It's not one of the common open source licenses, but it's certainly open source, with some permissions to modify and such.
Gnuplot is a portable command-line driven graphing utility for linux, OS/2, MS Windows, OSX, VMS, and many other platforms. The source code is copyrighted but freely distributed (i.e., you don't have to pay for it). It was originally created to allow scientists and students to visualize mathematical functions and data interactively, but has grown to support many non-interactive uses such as web scripting. It is also used as a plotting engine by third-party applications like Octave. Gnuplot has been supported and under active development since 1986.
It does 3D plotting as well, which matplotlib doesn't do, and it's been around a lot longer. The reason I thought of matplotlib first is that it's intended as a library for a higher-level language, not a stand-alone application, so I'm guessing it might a bit easier for you to read.
One other suggestion, just to get an idea of the sorts of things Mathematica is doing under the hood, is to look at the documentation for Plot. In particular, if you look at the available options, you can deduce things.
MaxRecursion Automatic the maximum number of recursive subdivisions allowed
Method Automatic the method to use for refining curves
PerformanceGoal $PerformanceGoal aspects of performance to try to optimize
PlotPoints Automatic initial number of sample points
From the MaxRecursion and PlotPoints, you can see that it's doing an initial sampling then somehow deciding which regions need to be subdivided (resampled) to get an accurate view of the plot. And from there on, it's magic: there is some Method for this, and a PerformanceGoal to guide it...
For MATLAB, because of its cross-platform requirement there is no alternatives as using OpenGL. MATLAB runtime is written in C++ and non-axis GUI uses Java Swing. Therefore MATLAB Plot is probably a C++/OpenGL/Swing mixture.
In reality MATLAB graphics is much less complex then a video game graphics. I think it is easier to find tutorials on video game graphics and then "downsize" it to MATLAB functionality, like drawing a single line with the same color.
The most important concept is probably Transformation Matrix.
Basically most programs that plot any type of graph (particularly any graphs of reasonable complexity) will use some type of third party libraries.
The specific library used would depend on the programming language that is being used.
For example:
For a .Net application you might use Crystal reports. http://en.wikipedia.org/wiki/Crystal_Reports
For Java you might use JFreeChart. http://www.jfree.org/jfreechart/
And so on...
You will likely find numerious libraries for whatever language you decide to code in.
If you want to accomplish this functionality in your specific project I suggest using a library especially if you are a beginner. The internal complexities of how these graph libraries are implemented would be significant because of many issues such as cross platform compatibility, graphic rendering optimizations (ie: making sure the graphics render quickly and ‘prettily’), the maths associated with the positioning of elements on the graph and so forth.
Lastly I doubt you will find specific courses in this subject (or require them) as again excluding VERY specific cases programmers will always use libraries that already exist.
Why code it yourself when someone has
already solved the problem for you?
A good place to start is to understand that there is a grammar to graphics and what you want to construct upon receiving a plot command is a symbolic representation of the graph. For Mathematica, you can do something like
FullForm[Plot[Sin[x], {x, 0, 2 Pi}]]
to see the internal representation Mathematica uses. Basically you need to describe the line segments (2D) or meshes (3D) you want to draw in terms of their color and coordinates. Also, there needs to information about the scale of the graph and how to draw tick marks, label axes, etc.
This leads us to the heart of the question, how do you determine the line segment you want to draw from a function and a range? If you dig around in the help file for plot, you see a few things. First there is a plot points option and a MaxRecursion option. This leads me to believe (and this is just an educated guess, but it is how I would do it) that Mathematica plots the initial number of points on an even interval over the range to get a starting value. The next part is to identify regions where change exceeds some threshold and then to sample more points until the "change" between any two points in your line segment is below a threshold. Mathematica does this recursively, hence the MaxRecursion option.
So far I have been pretty vague about defining rate of change. A more useful way to describe change is to take 3 pts on your line segment. Assume a linear relationship between the 1st and 3rd point and, assuming this linear relationship, make a prediction about what the 2nd point would be. If the error of this prediction is sufficiently low, then consider the next group of three points. If the error is above a threshold, then you should sample some more points in this region until the threshold is met. In this way you will require relatively few points where the curve is relatively straight and more at the "interesting" parts where it bends in new directions. The smoothness of the curve you draw will be proportional to the error you are willing to tolerate in the linear prediction of points.
This is really the very first try.. so all kind of suggestions are welcome. I am looking for software that recognizes a mathematical function from a bitmap / jpg. E.g. if you have the graph of some log(x) as jpg and you´d enter the x,y scales the program should tell that log(x) was used to create this. Maybe some OMR software might help, maybe it´s rather some math tool.
Is it possible at all?
If you have a bitmap - convert it to a 2 column data (for example "x y" of black pixels and ignore the white) set so that software can easily analyze it.
If you know the possible choice of functions that it could be (log, sin, exp) then you can use a simple minimization routine like Levenberg-Marquadt to fit a function and look at the fitness score (whichever one has lowest wins!)
If you have no idea what the function is - http://www.zunzun.com/
Good luck!
hi
you must creat a neural net(mlp or hopfield) then with a set of matrices:p for entry and t for target learning your net. after you sure of the performance of your net, you can use from yor net to recognize all picture(bitmap) that convert to a matrix. all of this possible in matlab, however you most first learn neural net.