What is Hiperbolia?

Hiperbolia is the hyperbolic city, it was built using hyperbolic geometry in a threedimensional space.
It's a virtual reality application that emulates the representation of a threedimensional model of hyperbolic geometry. It is also a virtual reality application in the sense of it's educational purpose.
The goal for building Hiperbolia is a better understanding of the behaviour of hyperbolic space using visual resources. This is the reason why Hiperbolia works very similiar to a videogame: it's a world to roam about and discover the marvells and rareness of hyperbolic geometry.
The sourcecode is written under the CC (Creative Commons) License, so anyone with a bit of understanding of C++ can create his own hyperbolic shapes. It's not easy though! The person who wants to become a builder in Hiperbolia will face the rules of hyperbolic geometry and will discover it's not that simple to build houses and streets. Learning will happen in other ways, rather than simply watching objects.
You will see Hiperbolia is Art. Well, at least strives to be. Graphic designers, musicians and artists in general, along with mathematicians and programmers have worked all the way down this project. Hiperbolia was planed to be a whole environment, with it's own music and visual design to immerse ourselves into this peculiar world. Even though we have tried to communicate something through Hiperbolia, it will be it's users who deem if it is art or not.

Techniques, technicalities and maths.

For building Hiperbolia, Klein's model of hyperbolic geometry was used. Although Klein's and Poincare's models are different, they describe the same space. This means that what the user is looking at is the hyperbolic space through Klein's model.
If you are looking for some formulas and maths abstraction of hyperbolic gemoetry, mathemathicians could go on about it for for ages. But I think that wouldn't be of much use when there's this. Besides, it's much clearer than what I could write here.
Computationally speaking, Hiperbolia is very consuming, not every computer will run it smoothly. But thats why the city is divided into sections, some of them being very computationaly consuming, while others are not so. Still, a computer with the following requirements would run it smoothly:
Processor: 3 cores, 2.2Ghz each.
Mem: 3Gb.
Video: Nvidia GeForce 8800 or later, Ati 3600 or later.
OS: Windows XP/Vista/7, any Linux, MacOSX 10.4 or later.

The graphics rendering engine used was OGRE www.ogre3d.org, which was picked because of its ease of use, power, materials and textures capabilities, and its cross-platform (really) arquitecture. The project was developed under Linux, but has been thoroughly tested in MacOSX and windows. OGRE made this possible. It runs under DirectX or OpenGL. Stereoscopy can be enabled in Windows. The sound system used was OpenAL. OIS was the input system.

Who created this software?

Ok! This project has been under development for 2 full years, and still is. It has been entirely developed by the Instituto de Matematicas de la Universidad Nacional Autonoma de Mexico. (That is The Institute of Mathematics of The Mexican Autonomous National University).
The credits would be as follow:
Director:
Dr Javier Bracho
Director of the Instute of Mathematics.

Coordinator:
Dr Michael Barot
Researcher of the Institute of Mathematics.

Mathematics and Design Assistant:
Mat Astrid Jaimen Lamas

Conceptual Design Aid:
Lic Dulce Aguirre Barrera

Programming and Desing:
Daniel Arevalo Rodil

The Laboratory of Virtual Reality from DGSCA UNAM has been specially helpfull all the time. And so has been the Ixtli Visualization from the same.

Music Composed by:
Lic Dulce Aguirre Barrera
Mus Miguel "Flux" from "NodLands Children"

Music Interpreted by:
Lic Dulce Aguirre Barrera
Mus Miguel "Flux" from "NodLands Children"
Leonardo Mariano Castro

Other persons invovlved somehow in the development of this project, particularly, in the computational development are:
Mat Monica Leñero from the Institute of Mathematics
Mat Eduardo Sacristan from the Institute of Mathematics
Mat Renato Leriche Vazquez from the Faculty of Science
Mat Carmen Ramos Nava from DGSCA
Mat Daniel Chavez from DGSCA

Download Page

Windows XP/Vista/7 Installer Beta 1.0 "Moni"

Finally!
Win XP/Vista/7 Self Installer

License

HIPERBOLIA by UNAM Daniel Arevalo Rodil is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.
Based on a work at www.hiperbolia.com.

Manual and Instructions

ARROWS->move
I->Euclidean fly up
K->Euclidean fly down
O->From Euclidean movement go back to hyperbolic movement
W->Hyperbolic fly up
S->Hyperbolic fly down
A->Go to hyperbolic floor
Y->Screenshot
E->Interact with object infront of you.
E->Enter doors and portals
C->If dialog, go to next dialog
C->Change height of camera from real hyperbollic height, to euclidean height.

Installation Instructions for Sourcecode

LINUX

Dependencies: Ogre 1.6.4 or later. OIS. CEGUI. OpenAL. alut or freealut

Uncompress tgz file

Enter directory

type in shell "./tomake" thats the script thats takes care of all compilation

Alut warnings will be issued, never mind them

If all goes well, enter ./bin directory and type "./hpbStreet"

Windows

Dependencies: Ogre 1.6.4 or later. OIS. CEGUI. OpenAL (32 or 64). alut. Direct X 9 or OpenGL. Visual Studio 2008 (though other versions may work... im particularly sure 2005 works)

Uncompress file wherever you want

Open Visual Studio and Create a new C++ empty project

On headers right click, choose "add existing item" and load all *.h files in the hiperbolia directory

On sources right click, choose "add existing item" and load all *.cpp files in the hiperbolia directory

Right click on the project and open its properties. Choose "Release" from the menu at the top

Under C++->General in Additional Include Dirs, add the folder where all hiperbolia sourcode is. Afterwards add all necessary directories for the dependecies. That means adding the include dirs of OGRE, OpenAL, OIS, alut and thats about it.

Under Linker->General in Additional Linker Libs add the folders where the .lib files for the Dependencies are.

Under Linker->Input in Additional Dependencies add the following:
OgreMain.lib
OIS.lib
OpenAL32.lib (or 64)
alut.lib

If all goes well... building the solution should be a success...

If not please let me know!! As i have said, im working on the installer but i haver never in my life done an installer so bare with me!

If success... enter your Visual Studio project directory with your file explorer, under the Release folder, there should be an executable .exe file with the name of your project.

Copy this executable, to the folder named "bin" inside the hiperbolia folder

From that location, "bin", run the program... and the Ogre dialog should appear...

If all goes well

If all has gone well, you should see 5 doors, flying in the middle of nowhere and a post with an spectacular saying welcome to hiperbolia city.

To enter a door, put the camera infront of it and type "E". If you enter a new part of the city, there will be an overlay with an explanatory text about this particular world... by pressing "C" you can go to the next dialog... until you enter the world. Mind you, it takes a bit to load the big parts of the city... no more than 2 mins though.

Now, the doors at the entrance take you to all five possible worlds in hiperbolia... from left to right they are:
The Hiperbolia Cactus Garden (no to impressive)
Astray (our first tesselation 5:4 to work)
Tessel (its too curved to be intuitive and has some mistakes)
Ugly (the first world we created and the most curved)
Trua (the biggest world, and the most accurate)

The Hiperbolia Garden, Astray, Ugly and Trua are all interconnected through red energy portals, which you enter through by pressing "E". There are two other worlds, the Necropolis, accesible through Trua, and the Room of Urania, accessible through Astray

NOTE Hiperbolia might seem strange and pointless at first, but try flying hyperbolicaly and euclideanly, and seeing what happens. I as the programmer, can tell you Hiperbolia its very strange... but its not easy to see whats going on. (Imagine how many headaches did I achieve to make the easiest things be mathematically correct). For a start go to Astray, and see that you have to turn around 5 times (90 degrees) each around a building in order to be at the place you started...

Hope you enjoy it :)