Math

Symmetry Breaking in Automated Planning

This is my master thesis about exploiting structures in automated planning (through symmetry breaking). You can read it here: Exploiting structures in automated planning. The domains and problems, that were used for testing, are here: Domains.

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Viterbi Algorithm Clarified

All articles about Vitebi algorithm, which I found, seemed too complicated and hard to understand. They either had too much theory and no examples, or too complex example without an abstract description. I will try to write a my own article and clarify things a little.

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Monty Hall problem makes no sense, or does it?

It has been 8 years since I heard about Monty Hall problem for the first time. I never completely trusted the offical solution. The only solution I would completely trust is my own simulation of thousands of games, so I decided to make one and prove the rest of the world wrong.

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Introduction to Metamath

Official Metamath description has 211 pages. This is a "shrinked" version, which does not contain introduction to logic, history of logic, definitions and statements, that mathematicians and computer scientists are already familiar with. Explore it in MM Tool.

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Taylor polynomial clarified

I decided to write this article, because all other articles I found on the internet seemed too complicated and did not explain the basic principles. I will avoid formalism, but I am sure formalisms will be clear to you after reading this article.

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Fastest Gaussian Blur (in linear time)

I needed a really fast Gaussian blur for one of my projects. After hours of struggling and browsing the internet, I finally found the best solution.

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Interpolation with Cubic Splines

Adobe Photoshop, Gimp and many other image editors have a tool called Curves. There are several "knots" and while you move them, it computes a curve in between. I always wondered, how is this curve computed.

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Binary relations and closures

I have made a little tool. Here you can specify some binary relation over a finite set. Then you can generate a closure of it.

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Fortune’s algorithm and implementation

This text was created as a credit work at subject Algorithms nad data structures II, MFF UK. It contains an implementation in C++ (at the end) and ActionScript 3.0 (in previous posts).

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Voronoi diagram in JavaScript

I always wanted to try programming in JavaScript, so I decided to rewrite my implementation of Fortune's algorithm from C++ and ActionScript 3 into JavaScript.

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Solving sliding puzzle with Prolog

This work has been created as my credit exam at subject Nonprocedural programming at MFF UK. It is about solving sliding puzzle with Prolog programming language.

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Basic geometry functions

In this article we will see how to implement some basic geometry functions in 2D space. We will wirte line segment intersection and circumcircle.

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Force-based 3D graph drawing in AS3

I decided to extend my last graph drawing algorithm - I added a "z" coordinate (for position, forces etc.). I used Away3DLite libraries for drawing a graph.

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Force-based graph drawing in AS3

This post will be dedicated to drawing graphs in an aesthetically pleasing way. We will use physics "spring" algorithm, and create real-time simulation.

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Sierpinski Triangle in AS3

Today we will take a look at recursive fractal drawing in ActionScript 3. We will draw a Sierpinski Triangle.

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Lightweight fast matrix class in C# (Strassen algorithm, LU decomposition)

This is lightweight (19 kB) matirx class written in C#, that includes basic matrix operations.

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