Thursday, April 30, 2009

3D Supershape

Over the last few years I was looking into the 3D Supershape formula described by Paul Bourke here and originally developed by Johan Gielis. I love the shape of the objects that are a result of those and therefore I always wanted to use it to create my own demos after I saw the one from Jetro Lauha ( Here is my first attempt to generate C source out of the equations:

Suitable C pseudo code could be:

float r = pow(pow(fabs(cos(m * o / 4)) / a, n2) + pow(fabs(sin(m * o / 4)) / b, n3), 1 / n1);

The result of this calculation is in polar coordinates. Please note the difference between the equation and the C code. The equation has a negative power value, the C doesn't. To extend this result into 3D, the spherical product of several superformulas is used. For example, the 3D parametric surface is obtained multiplying two superformulas S1and S2. The coordinates are defined by the relations:

The sphere mapping code uses two r values:

point->x = (float)(cosf(t) * cosf(p) / r1 / r2);
point->y = (float)(sinf(t) * cosf(p) / r1 / r2);
point->z = (float)(sinf(p) / r2);

Because r1 and r2 had a positive power value in the C code above we have to divide by those variables here. Here is a Mathematica render of this code:

Wednesday, April 29, 2009

Rockstar Games

Today GTA IV was launched a year ago and it is my last day where I am employed at Rockstar Games. After fantastic more than four years I felt like I should get a break to go back to some research topics and see my kids growing for a while :-), so I gave my notice two weeks ago.

Beagle Board

I got the whole development environment going and wrote a few small little graphics demos for it. All the PowerVR demos I tried ran on it nicely. Very cool!
If you are interested in a next-gen mobile development platform I would defitely recommend looking into this at

Any further development has now moved to lowest priority ... maybe at some point I will play around more with Angstroem. There is an online image builder

Monday, April 20, 2009 Ubuntu 8.04

In the last few days I setup a development environment for a BeagleBoard (see I wanted to hold the next-gen environment for future phones and the OpenPandora in my hands today. Overall the size of the board is astonishingly small and you can power it with the USB port. The board runs Angstroem -a Linux OS-, it has the OMAP3530 processor on there. It has a dedicated video decode DSP, the PowerVR SGX chipset, a sound chip and a few other things that I haven't used so far. You can even plug in a keyboard and a mouse and you have a full-blown computer with 256 MB RAM and 256 MB SDRAM.
To get this going I had to install a Linux OS on one of my PCs; Ubuntu 8.04. To relieve the pain of having to google all the Linux commands again and again I try to write down a few notes for myself here:
- minicom is not installed by default. You have to install it yourself. To do this you have to open up Applications -> Add/Remove and refresh the package list (you need an internet connection for this) and then install the build essentials first and then minicom by typing into a terminal:
sudo apt-get install build-essential
sudo apt-get install minicom
- to look for the RS232 serial device you can use
dmesg | grep tty
I found adding environment variables to the PATH statement different on Ubuntu 8.04. You can set an environment variable by using
export VARNAME=some_string
export PATH=$PATH:some/other/path
To check if it is set you can use
echo $PATH
For the PLATFORM you set it by typing
export PLATFORM=LinuxOMAP3
you use
to check if it is correct.
Similar for library pathes you type
export LIBDIR=$PWD
from the directory where the lib files are. To check that this works you can use
echo $LIBDIR
To make all those variable values persistent you can copy those statements at the end of the .bashrc file. Some other things I found convenient were:
gksudo gedit
start the editor with sudo.
Copying a file from one in another directory can be done by using the cp command like this
$ cp -i goulash recipes/hungarian
cp: overwrite recipes/hungarian/goulash (y/n)?

You can copy a directory path in the terminal by dragging the file from the file browser into the terminal command line.