## OpenGL Matrices – the missing bits

While generally the available documentation on how the OpenGL matrices work is quite good, there are some missing bits. Although not necessary for your everyday rendering, they give one some insight on how rasterization in general and OpenGL in special works.

# W coordinate after perspective divide

After conversion to normalized device coordinates(ndc) one might think each vertex looks like

$$\vec{v}_{ndc} = \frac{1}{w} \begin{pmatrix} x \\ y \\ z \\ w \end{pmatrix} = \begin{pmatrix} \frac{x}{w} \\ \frac{y}{w} \\ \frac{z}{w} \\ 1 \end{pmatrix}$$

however it looks more like

$$\vec{v}_{ndc} = \begin{pmatrix} \frac{x}{w} \\ \frac{y}{w} \\ \frac{z}{w} \\ \frac{1}{w} \end{pmatrix}$$

the $w$ coordinate is not divided by itself, but is inverted instead. This is done because the interpolation between vertices still needs to take place and for perspective correct interpolation one needs the camera space depth $z = -w_{cam}$.

$$\vec{v}_{\alpha} = \frac{(1-\alpha)\frac{\vec{v}_0}{-z_0} + \alpha\frac{\vec{v}_1}{-z_1}} {(1-\alpha)\frac{1}{-z_0} + \alpha \frac{1}{-z_1}} = \frac{(1-\alpha)\vec{v}_0 w_{0_{ndc}} + \alpha\vec{v}_1 w_{1_{ndc}}} {(1-\alpha) w_{0_{ndc}} + \alpha w_{1_{ndc}}}$$

instead of dividing by $-z$ we can multiply with $w_{ndc}$ as multiplication is faster than division.

Note that for brevity the given formula assumes a scanline based rasterizer as it interpolates only between two vertices. The general approach is to use barycentric coordinates to interpolate between all three vertices simultaneously.

# Row major or column major

Even though even Wikipedia says OpenGL is column major, it is actually storage agnostic. However by default it interprets your 16 element array as:

$$\begin{bmatrix} m_0 & m_4& m_8 & m_{12}\\ m_1 & m_5& m_9 & m_{13}\\ m_2 & m_6& m_{10} & m_{14}\\ m_3 & m_7& m_{11} & m_{15} \end{bmatrix}$$

Yet most OpenGL functions dealing with matrices offer a transpose parameter which you can use to specify the used order. For a comparison of storage orders see the Eigen documentation.

## Using the XBox Controller with Ubuntu (the modern way)

If you want to get your Xbox One/ Xbox 360 running on ubuntu you basically have the choice between the in-kernel xpad driver and the userspace xboxdrv driver.

Most of the guides recommend using xboxdrv as xpad has been stagnating. However using xboxdrv has some disadvantages; as it runs as a daemon in userspace you have to manually take care of starting/ stopping it and giving your user access to the virtual devices it creates.
Xpad on the other hand just works as any other linux driver directly inside the kernel which is more  efficient and hassle free.

Fortunately while pushing SteamOS Valve has updated the xpad driver bringing it on par with xboxdrv:

• they added support for Xbox One Controller
• they fixed the communication protocol – no more blinking controller light

You can get the improved SteamOS driver from this PPA. Just install the steamos-xpad-dkms package and everything should just work.

## How to draw a line interpolating 2 colors with opencv

The build-in opencv line drawing function allows to draw a variety of lines. Unfortunately it does not allow drawing a gradient line interpolating the colors at its start and end.

However implementing this on our own is quite easy:


using namespace cv;

void line2(Mat& img, const Point& start, const Point& end,
const Scalar& c1,   const Scalar& c2) {
LineIterator iter(img, start, end, LINE_8);

for (int i = 0; i < iter.count; i++, iter++) {
double alpha = double(i) / iter.count;
// note: using img.at<T>(iter.pos()) is faster, but
// then you have to deal with mat type and channel number yourself
img(Rect(iter.pos(), Size(1, 1))) = c1 * (1.0 - alpha) + c2 * alpha;
}
}

## Introducing Sensors Unity

Sensors-Unity is a new lm-sensors GUI for the Unity Desktop. It allows monitoring the output of the sensors CLI utility while integrating with the Unity desktop. This means there is no GPU/ HDD support and no plotting.
If you need those you are probably better suited with psensor. However if you just need a overview of the sensor readings and if you appreciate a clean UI you should give it a shot.

Sensors Unity is available from this PPA

It is written in Python3 / GTK3 and uses sensors.py. You can contribute code or help translating via launchpad.

# Overview

In contrast to other applications the interface is designed around being a application. Instead of getting another indicator in the top-right, you get an icon in the launcher:

The idea is that you do not need the sensor information all the time. Instead you launch the app when you do. If you want to passively monitor some value you can minimize the app while selecting the value to display in the launcher icon.

To get the data libsensors is used which means that you need to get lm-sensors running before you will see anything.

However once the sensors command line utility works you will see the same results in Sensors-Unity as it shares the configuration in /etc/sensors3.conf.

# Configuration

Unfortunately configuring lm-sensors via /etc/sensors3.conf this is quite poorly documented, so lets quickly recap the usage.

• /etc/sensors3.conf contains the configuration for all sensors known by lm-sensors
• however every mainboard can use each chip in a slightly different way
• therefore you can override /etc/sensors3.conf by placing your specific configuration in /etc/sensors.d/ (see this for details)
• you can find a list of these board specific configurations in the lm-sensors wiki
• to disable a sensor use the ignore statement
• #ignore everything from this chip
chip "acpitz-virtual-0"
ignore temp1
ignore temp2
• to change the label use the label statement
• chip "coretemp-*"
label temp1 "CPU Package"

## Sensors-Unity Specific Configuration

Sensors-Unity allows using the Pango Markup Language for sensor labels. For instance if you want “VAXG” instead of “CPU Graphics” to be displayed, you would write:

label in4 "V<sub>AXG</sub>"

In order not to interfere with other utilities and to allow per-user configuration of the labels/ sensors Sensors-Unity first tries to read ~/.config/sensors3.conf before continuing with the lm-sensors config lookup described above.

## introducing sensors.py

sensors.py is a new python wrapper for libsensors of the lm-sensors project. libsensors is what you want to use to programmatically read the sensor values of your PC with Linux instead of parsing the output of the sensors utility.

sensors.py is not the first wrapper – there are two alternatives, confusingly both named PySensors.

PySensors (ctypes) follows a similar approach to sensors.py by using ctypes. However instead of exposing the C API it tries to be a object-oriented(OO) abstraction, which unfortunately lacks many features and makes the mapping to the underlying API hard. Furthermore it does not support Python3.

PySensors (extension module)  does not use ctypes and thus is more efficient, but if you write a python script probably compiling a extension module is worse than losing some performance when reading the values.
Additionally there is python3 support and also some OO abstraction. The latter is somewhere in between the C API and proper OO: sensors_get_label(chip_name, feature) is ChipName.get_label(feature) instead of feature.get_label().

So what makes sensors.py immediately different is that it does not try to do any OO abstraction but instead gives you access to the raw C API. It only adds minor pythonification: you dont need to mess with pointers, errors are converted to exceptions and strings are correctly converted from/ to utf-8 for you.

However working with the C API directly is tiresome at times – therefore there is also an optional iterator API, which is best shown by a demo:

import sensors

sensors.init()

for chip in sensors.ChipIterator("coretemp-*"):

for feature in sensors.FeatureIterator(chip):
sfi = sensors.SubFeatureIterator(chip, feature)
vals = [sensors.get_value(chip, sf.number) for sf in sfi]
label = sensors.get_label(chip, feature)

print("\t"+label+": "+str(vals))

sensors.cleanup()

result:

coretemp-isa-0000 (ISA adapter)
Physical id 0: [38.0, 80.0, 100.0, 0.0]
Core 0: [37.0, 80.0, 100.0, 0.0]
Core 1: [35.0, 80.0, 100.0, 0.0]
Core 2: [38.0, 80.0, 100.0, 0.0]
Core 3: [36.0, 80.0, 100.0, 0.0]


for a more sophisticated example see the example.py in the repository.

## Replacing your desktop laptop with a ITX workstation

If you use your laptop as a desktop replacement, you will at some point get an external display and a mouse/ keyboard for more convenient usage.
At this point the laptop becomes only a small case of non-upgradable components.

Now you could as well replace your laptop by a real case of comparable size.  This will make your PC not only easily upgradable, but allow higher-end components while being more silent at the same time.

## Streaming the Screen on Android

In this post I want to discuss way of getting the screen content of your Android device to the TV or monitor. If you wonder why one might want to do such a thing – just think about playing some Android games with a bluetooth gamepad or watching a movie where your PC is not available.

Specifically I want to introduce SlimPort. SlimPort is a feature of Nexus devices which is unfortunately not covered much in reviews.
Basically SlimPort is DisplayPort over the Micro-USB connection of your device allowing you to mirror its display.

# But the future has arrived: we got Miracast!

One might wonder why one should go through the hassle of using a old-school HDMI cable.

# Building the program

To trigger a rebuild of the program simply execute

dpkg-buildpackage

To upload a package to a PPA you first need to sign it to prove that you are the author. To do this you have to execute the following in the <packagename>-<newversion> directory

debuild -S

sudo apt-get install dput

Now change to <somedir> and execute

dput ppa:<your_username>/<repository> <source.changes>