A web server on a Raspberry Pi

I recently bought a Raspberry Pi mini-computer.

Here I offer a small tutorial for those trying to use it as a simple web server.
This will assume you already built your raspberry pi box with Raspbian installed in the SD card.

I compiled a list of recipes from different websites and pages, in the hope that this will be useful to someone with a similar setup as mine (a macbook with OS X and a wifi router at home.)

You don’t need your pi to be connected to an external monitor and keyboard to make it work. If your pi came with the Raspbian OS then it’s prepared to be accessed through SSH out of the box.

Connect your pi to your router with an ethernet cable or set up your wifi connection (you need to enable wifi first on your pi.) Then you need to find out which internal IP was the raspberry assigned to by your router, and then ssh with user pi and password raspberry. To find the IP of your pi you can check on your router settings, the DHCP Client List. Your pi should be named raspberrypi or similarly.

In principle it’s not guaranteed that the IP will be the same every time the device connects, but in my experience with my router, the IP assigned to each device is always the same.

The first time you log in you will be greeted with a setup menu. I suggest you follow the instructions on this site to get it up and running. Most importantly, change the default password to log in!

Once you know your pi’s IP (in my case was, yours may differ) you can log in normally.

ssh pi@
password: raspberry

Installing Apache 2

The following are steps to install an Apache server on your raspberry pi. Apache is a popular web server in the Linux side of computers. Another emerging contender on the open source side is Nginx (pronounced ‘Engine X’), but I have no experience with it. I should probably buy another pi and try this new server; after all, one of the advantages of the pi is the relatively inexpensive hardware!

Back to Apache, installing it is relatively easy, you just type

sudo apt-get install apache2 apache2-doc apache2-utils

on the terminal and that should be enough.

Test Apache with a simple html page

You can manage several sites on your pi with Apache, all available sites are stored in files under /etc/apache2/sites-available, of those you can enable or disable the ones you like with the commands a2ensite and a2dissite (a2 is for apache2 and the rest is enable/disable site.) These commands basically create and delete symlinks into /etc/apache2/sites-enabled.

Go to /etc/apache2/sites-available. We’ll make a test page to confirm apache is running well. First we copy the default site provided by apache to have a template to work with.

sudo cp default test

Edit the test file replacing instances of “/var/www” to “/home/pi/www”
and create a simple welcome index.html in /home/pi/www

Below is an example of a simple html. If emacs is your preferred command line editor, you will have to install it now, because Raspbian doesn’t include it by default.

sudo apt-get install emacs

then you can create index.html with emacs on /home/pi/www

mkdir www
emacs www/index.html

and copy the following text in it.

<p>Website coming soon</p>

Then execute the following commands to enable the site (a2ensite), disable the old site (a2dissite) and reload the sites.

sudo a2ensite test
sudo a2dissite 000-default
sudo service apache2 reload

You should see the Welcome page you set up in /home/pi/www, when you visit the pi’s IP (type on your favorite web browser)

If you want to access your website from outside your internal network (given by your router) you need to direct the external HTTP requests on port 80 to your raspberry pi’s port 80.

If you’re connected through Wifi like I am, then you have a wireless router and you have to configure your router to do the redirection. Select incoming port 80 to map to your pi’s internal IP’s ( in my case) port 80.

Once you do that, you can access your website through your IP (the one provided by your ISP) on the web browser. You may want to hire a Domain Name Service to assign your IP number to some memorable web address. Some websites offer this service for free, noip.com is one of them.

Please leave comments if you find typos or mistakes!

A web server on a Raspberry Pi

Craster’s Incestual Recursion

Black Holes and Revelations

He marries his daughters, and they give him more daughters, and on and on it goes.
Edison Tollett

During one of my usual afternoon discussions with fellow graduate students, we strayed on the precarious path of incest and argued as to where incest would fit on the nature vs nurture spectrum. I preferred to attribute the cultural embargo on incest to nurture, as incest had been widespread in antiquity, whereas my friend was of the opinion that the incest taboo is hard-wired in human beings, citing the near-universal forbiddance of sexual relations within close family.

This made me wonder about the sustainability of a population where the only means of population growth (for whatever reason) is incest. Those of you who watch/read Game of Thrones will be able to think of just such a population, the Craster’s keep. Craster (who the above quote refers to) is an old…

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Craster’s Incestual Recursion

Stupid const, stupid mutable, stupid C++

code monk

Every now and then someone drags me into a C++ discussion. I have friends who code in C++. Some of them do it for money. I’m sorry about that.

Recently I heard about “const methods”. “What’s that?” I ask; “Methods that are contractually obliged not to change their object.”. Oh, I think. That seems really useful, but a feature like that would never make into C++ (I reason, based on what I know of C). Still, not knowing much about C++ I shut up and go and learn some more C++ instead. I consult my friends who actually know more C++ than I do. The replies are not consistent, not confident, and sometimes go all slippery and vague when I press for details.

Then, it dawns on me. A “const method” is simply a method whose this pointer is const qualified. It’s an inevitable feature of the language…

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Stupid const, stupid mutable, stupid C++

A Camera Class

For those like me that are interested in Game Development as a hobby, one of the main challenges to build a 3D game is understanding the OpenGL framework.

The distinction between the different coordinates systems is mandatory if one doesn’t want to get ultimately lost in coordinates transformations. A world coordinate system is a system of coordinates with which the scene is best described. It is the system that arises naturally from the game constrains and scene. The eye coordinate system is the system OpenGL understands, with the z coordinate sticking out from the screen and x and y running along the screen edges.

Even further, we also need a camera in our scene, that will be the point of view from where we render the scene.

It is very useful to split an OpenGL program into things our virtual objects do in the scene and how the camera moves in the scene. To achieve that split of responsibilities, it is necessary to have a Camera class that encapsulates the state of the camera at all times. The camera should know how to return its view transformation matrix to modify the point of view from which the objects will be rendered. This camera or view transformation will be the matrix that transform the vertices from the world coordinates to the eye coordinates.

For the impatient: a direct link to the github repository containing the Camera Class implementation on Objective-C can be found on this link. It can be easily modified for C++.

This article will try to explain hot to set a view transformation for a Camera class.

One way to implement a camera is to set the position and orientation of the camera in world coordinates. With this one can work out the transformation matrix to be applied to the vertices on the scene. The following will assume that we have a vector that points where the camera is looking at (lookAt), an approximate vector for what is considered “up” in the camera (upVector), and the coordinates of the camera (pos) on the scene. All three vectors in world coordinates. The upVector doesn’t necessarily must be the true upwards vector. It only must have a non-zero component along the true “up” direction.

In what follows, {i, j, k} are the basis vectors of the world coordinate system and {i’, j’, k’} are the basis vectors of the eye coordinate system. In the eye coordinate system -the only one that OpenGL cares about- the eye is always pointing in the -z direction. From the pos and lookAt vectors, we can find what is the k’ direction of the camera in world coordinates.

k’ = normalize(lookAt – pos)

k’ = normalize(poslookAt)

“Up” is in the y direction in the eye coordinate system. The upVector would be j’ if it weren’t for the fact that it’s not necessarily completely upwards. Nevertheless, the cross product between upVector and k’ will be i’, as long as upVector has a component in the true j’ direction.

i’ = normalize(upVector x k’).

Finally the cross product of k’ and i’ will give us the true j’.

j’ = k’ x i’

Now that we have the relative orientation of the camera {i’, j’, k’} with respect to world coordinates {i, j, k} we can figure out the transformation (it’s a rotation) between the two frames. This can be done easily noting that i’ = (i’.i) i + (i’.j) j + (i’.k) k etc. which can be written formally (it’s not a true matrix-vector multiplication)

\left[ \begin{array}{c}    i' \\    j' \\    k'    \end{array} \right]    = \begin{bmatrix} i'.i & i'.j & i'.k\\    j'.i & j'.j & j'.k \\    k'.i & k'.j & k'.k    \end{bmatrix}    \left[ \begin{array}{c} i \\    j \\    k \end{array} \right] =    \left[ \begin{array}{c} i' \rightarrow \\    j' \rightarrow \\    k' \rightarrow \end{array} \right]    \left[ \begin{array}{c} i \\    j \\    k \end{array} \right] \equiv R \left[ \begin{array}{c} i \\    j \\    k \end{array} \right]

where i' \rightarrow means write the components of i’ in the {i,j,k} base in that row. For any other vector (x’,y’,z’) the transformation is the same. It can be seen by writing

\begin{array}{l} v = x' i' + y' j' + z'k' = (x',y',z') (i', j', k')^t = (x',y',z') R (i, j, k)^{t} = (x,y,z).(i, j, k)^t \\    \Rightarrow (x',y',z') R = (x,y,z) \\    \Rightarrow (x',y',z') = (x,y,z) R^t \\    \Rightarrow (x',y',z')^t = R.(x,y,z)^t    \end{array}

(R^t=R^{-1} since it is an orthonormal matrix).

R is the rotation that takes a vector from world coordinates to eye coordinates. Its transpose will take from eye to world coordinates. To put the camera in the world we did two operations. First we rotated the camera at the origin by matrix R^t and then we translated it by vector pos.

Mcam = T(pos).RT

The matrix we have to apply to vertices to simulate the camera motion is the inverse of this Mcam

Mv = R . T(-pos)

Implementation in OpenGL|ES:

OpenGL|ES stores the matrices in a column-major format. (We can equivalently think that it stores the transpose of the matrix in a row-major format.) To construct the matrix R, we have to fill each row with the primed direction versors in the array R[16].

\left[ \begin{array}{c}    i' \rightarrow 0 \\    j' \rightarrow 0 \\    k' \rightarrow 0 \\    0 \ldots 1    \end{array}    \right] =    \begin{bmatrix} R_0 & R_4 & R_8 & R_{12} \\    R_1 & R_5 & R_9 & R_{13}    \\ R_2 & R_6 & R_{10} & R_{14}    \\ R_3 & R_7 & R_{11} & R_{15}    \end{bmatrix}

 for (int i = 0; i &lt; 3; i++) {
   for (int j = 0; j &lt; 3; j++) {
     viewMatrix[i*4 + j] = prime[j][i];
   viewMatrix[i*4 + 3] = 0.;
 for (int i = 12; i &lt; 15; i++) viewMatrix[i] = 0.;
 viewMatrix[15] = 1.;

The translation as an array T[16] is the usual one and has the form:

\begin{bmatrix} 1 & 0 & 0 & t_x    \\ 0 & 1 & 0 & t_y    \\ 0 & 0 & 1 & t_z    \\ 0 & 0 & 0 & 1    \end{bmatrix} =    \begin{bmatrix} T_0 & T_4 & T_8 & T_{12} \\    T_1 & T_5 & T_9 & T_{13} \\    T_2 & T_6 & T_{10} & T_{14} \\    T_3 & T_7 & T_{11} & T_{15}    \end{bmatrix}

But since T is mostly empty we can make the multiplication R.T without storing the array T. The rotation block will remain untouched and R_{12}, R_{13}, R_{14} will be replaced by a linear combination of the rotation terms and the translation terms.

\begin{array}{l} R_{12} \leftarrow t_x R_0 + t_y R_4 + t_z R_8 \\    R_{13} \leftarrow t_x R_1 + t_y R_5 + t_z R_9 \\    R_{14} \leftarrow t_x R_2 + t_y R_6 + t_z R_{10}    \end{array}

In code:

 viewMatrix[12] = - position[0] * viewMatrix[0] \
                  - position[1] * viewMatrix[4] \
                  - position[2] * viewMatrix[8];

 viewMatrix[13] = - position[0] * viewMatrix[1] \
                  - position[1] * viewMatrix[5] \
                  - position[2] * viewMatrix[9];

 viewMatrix[14] = - position[0] * viewMatrix[2] \
                  - position[1] * viewMatrix[6] \
                  - position[2] * viewMatrix[10];

The whole project (WIP) can be found on this link: https://github.com/martinberoiz/CameraClass

Note: I will update this post with more details.

A Camera Class

Sorting Algorithms and the Strategy Design Pattern

There’s an excellent course on Algorithms in the Coursera website. You should go check it out. It is a series of videos and exercises on several well known basal algorithms in Computer Science. If you are not a CS major, but you program as part of your daily routine, I recommend you at least watch the videos, since they are very informative.

Even though the language they use to implement the algorithms is Java, I decided it would be a good exercise for me to try them in C++. I am not particularly fond of C++, but I thought it would be an opportunity to explore more the language.

The first set of algorithms deal with sorting arrays of various types. I think that’s an excellent use case for the Strategy Design Pattern, in which each different sorting method is encapsulated into a subclass of a general ‘sorting’ class. This allows each strategy (method) to share the same outlets and they can be interchanged even at runtime if necessary.

Each individual strategy and its superclass Strategy class are all templates, to allow for sorting of different types of elements (double’s, int’s).

Each strategy will have a name() method that returns a string with the name of the method, a sort() method that does the trick, and a few other class methods.

Helper functions for a particular sorting method, should be kept private so we don’t contaminate the public scope of the strategies and possibly confuse the user of the class.

With the Strategy Pattern we can iterate over sorting strategies (like Selection Sort, Quick Sort, Merge Sort, etc).

In the following example, I have a simple test function called sorttest() that will take a strategy and an array of numbers (called ‘array’ in the code) and will test if the given strategy correctly sorts the array.

The sorting test for a vector of strategies can be done in one loop as is shown below:

 for (typename vector<SortStrategy<T>*>::iterator aStrat = allStrats->begin();
      aStrat != allStrats->end();
   T* data_copy = (T*)malloc(len*sizeof(*array));
   memcpy(data_copy, array, len*sizeof(*array));
   bool pass = sorttest(data_copy, len, *aStrat);
   printf("Test%spassed.\n\n", pass ? " ": " not ");

In summary, the Strategy Design Pattern is very useful in cases when one task can be accomplished in many different ways and one wants to abstract the method to do the task. Pluggable classes are neat!

A copy of my code using the Strategy Pattern and the Sorting classes can be found in this repository https://github.com/martinberoiz/algorithms.

Sorting Algorithms and the Strategy Design Pattern

The percolation problem

The percolation problem deals with connected paths between nodes in a 2D grid. The grid nodes could be in either of two states: “open” or “closed”; “conducting” or “insulating” or any other two opposite physical properties. When open, a node will connect with all the open nodes surrounding it. The system percolates where there is a path of connected nodes from any node on the top row to any node at the bottom row.

The system can be used to model diffusion of a liquid through a porous surface or the electric conductivity of a dielectric.

In the case of liquid diffusion, the grid is said to percolate when there is a connected path from any of the sites at the top row to any of the sites at the bottom row. On that moment, there is a free path for the liquid to move through the grid.

For a given grid size and a given fraction of open sites, there is a certain probability that the grid will percolate. It depends, of course, of the distribution of open sites on the grid.

It turns out that there is a phase transition on the probability of percolation of a two dimensional grid. Below a certain fraction of open sites, the probability of percolation is almost null. Above that fraction, the probability of percolation is almost certain. The percent value that divides both phases is very hard, if not impossible, to find theoretically. A good algorithm to simulate percolation for random grids is in need, to experimentally find this value.

The fast O(N lgN) algorithm to check for connected paths used in Sedgewick‘s Algorithm book is Quick Find or some optimized version of it.

I decided to implement myself these algorithms on C++, using the OO Strategy Pattern.

When I finished coding these command line tests, I thought it would be fun to see it in action for some concrete instance of a grid. That’s why I programmed a simple GUI for OS X.

The MVC (Model-View-Controller) was of great help here. Since I had my strategy classes for Quick Union, Quick Find and Weighted Quick Find as separate classes, I already had my model part done.

I then coded an Objective-C wrapper for the grid. This will be the class aware of the 2D nature of the grid. The model only knows about nodes, but it’s not spatially aware.

I only needed a general controller class, the application delegate provided by Xcode, and a view class to display the grid.

Once all the connections were done, I only added some bells and whistles to the app, and it was done.

An OS X GUI for a Percolation example
An OS X GUI for a Percolation example

I leave here a link to download the app, and I will post the source code in another post.


I hope you enjoy it!

The percolation problem

Mail.app behaving strangely in Mavericks

I found recently that Apple’s Mail.app was behaving erratically: the notification for unread emails wouldn’t disappear, even after reading all emails; junk email was properly marked as such, but refused to go into the spam folder and the rules I had set for certain senders didn’t work.

It all started after I signed up for iCloud to synch all my email accounts. That should have been my first clue to what the problem was, but it took me some time to realize what was going on. It turns out that iCloud is not smart enough (yet?) to realize that some of the synched accounts were already in place locally on my machine. It would then duplicate my locally set accounts with those from iCloud.

The problem went away once I removed those duplicates causing the problem. I still haven’t decided wether I want all my email accounts in the cloud. I don’t need all of them in all of my devices (I don’t really check all my emails on my iPhone, for example.) So, I decided to keep my most used accounts in the cloud and keep the less used ones on the MacBook that I use most frequently.

If you have the same problem, you should check your “Internet Accounts” in System Preferences and remove those you don’t want them there.

Mail.app behaving strangely in Mavericks