on nice lecture about Delaunay triangulation and Voronoi diagrams .Only the basics are included .

DT

some art mathematics again

 

 

some art always is great … Willem Besselink creates these surface meshes from 3D plots yeah

 

TOR-PROJECT

tor-project is a useful tool for keep your anonymity .Spying from google , facebook and others threats of our privacy. Tor is a network of virtual tunnels that allows people and groups to improve their privacy and security on the Internet.

An easy way to have some privacy , or at least give a try is TOR  ,which prevents the sites you visit from learning your physical location ,changing your ip-adress and to browse the Internet anonymously.

For windows it’s easy , but for us poor debian-xfce users who prefer to use google-chrome it’s not ! So there are two ways of using tor alongside with chrome :

a) use firefox

b)try GNOME instead !

there are some issues for chrome at XFCE and you must configure GNOME  because changing proxy settings at chrome looks a bit difficult. Chromium/Chrome do not recognize the xfce desktop session as gnome but adding at ~/.bashrc :

export GNOME_DESKTOP_SESSION_ID=default

doesn’t solve the problem either …
anyway looking for some details missing , maybe make it work finaly …

installing tor will need also polipop , and proxy switchy but vidalia is not needed , step by step here

a little bit of geometry from USSR with love

In the interior of a 12-gonal convex (a polygon with 12 vertices in 2D ) , there exists two points with distance 10cm. Let , the two interior points and  ,be the sum of the distances of the 12 vertical points respectively.Prove that

kind of refinement tri-elements :P

 

 

 

 

 

from http://www.sciencedirect.com/science/article/pii/S0306454909003752

happy new year !!!

from commandlinemagic :
while [[ $(date +%Y) -ne 2013 ]];do figlet $(($(date -d 2013-01-01 +%s)-$(date +%s)));sleep 1;clear;done;figlet 'Happy New Year!'

2012 space review

SpaceX docks with ISS  (photo below) ,  Astronomical unit gets redefined , Exoplanet next door , Asteroid miners open for business , Transit of Venus ,Neil Armstrong dies  and others here .

Delaunay Triangulation

it’s official for Wikipedia : divide and conquer algorithms are the faster for Delaunay triangulation ,so to celebrate let’s talk about this specific algorithm for the triangulation of a set of points (2D or 3D) which is called grid and is used in many aspects of scientific computing.

DELAUNΑY TRIANGULATION

DT combines several quality measures : maxmin angle condition,minmax constrained circumcenter etc .DT of a point set is the planar dual of the Voronoi diagram.The Voronoi Diagram is a partition of the plane into polygonal cells, each of one assinged to an initial point., so that the cell for input point P consists of a region fo the plane closer to P than any other input point.Any point (nodal-point of the grid) lies outside the circumcentre and hence any vertex of the Voronoi diagram has degree 3 and the DT will be a triangulation.

There are many algorythms for DT.Some of them have to do with the Convex hull of the set points.The main idea goes like this : Lift each point of the input to a paraboloid in one dimension up (for 2D it will be 3D) ,by mapping the point ,to the point .The convex hull of the lifted points can be divided  into lower and upper parts: a face belongs tho the lower convex hull if it is supported by a plane that separates the point set from .It can be shown that the DT of the input points is the projection of the lower convex hull onto the xy-plane:

Many algorythms of run-time are developed for DT.One nice one and pretty understanding is devide_and_conquer .For the generall overview of the most famous algorythms for DT and their run-time comparison is triangulation_algorythms_sigkrisi.

SOURCE CODE

you can try to compute the delauney triangulation from source code for your input data points from here (Fortran 90,C,C++)

Galois #3

i wrote some of the very-very basics of field extensions , in fact the examples help to  understand what an extension from a field to another is.field_extensions

the universal art of networking

Artist and architect Tomás Saraceno produces stunning installations that highlight the complexity in our interconnected universe and give vent to his obsession with aerial citie see these amazing photos