If you ever need more precision than what 15 decimal digits of the double format can offer, and arbitrary-precision arithmetic is too slow, too heavy, or simply not available, there is a neat trick: glue two doubles together and treat them as one number. This gives you ~31 decimal digits for roughly 9x the cost of a plain double in a real kernel (4-12x per isolated operation), with no heap allocation and no dependencies, which lands it almost exactly halfway between a double and a real arbitrary-precision library. This post explains the error-free transformations that make it work, measures it against MPFR, and shows where the trick runs out of steam.

Execution of C# code in Unity's Mono runtime is slow by today's standards, much slower than you might expect! Our game runs 2-3x faster on modern .NET compared to Unity's Mono, and in a few small benchmarks I measured speedups of up to 15x. I've spent some time investigating what's going on and in this article I will present my findings and why everyone should want Unity's .NET modernization to become production-ready as soon as possible.

Some time ago, I encountered and resolved a truly bizarre issue: certain players were unable to save their game due to an IOException with the error message "Success". To this day, I still receive inquiries from fellow devs about how to address this problem. This article documents the issue and provides a reference for the workaround.

Majority of our devices today can display 16.7 million colors. This may sound as a lot but sometimes human eye can notice a difference between two neighboring colors. I have encountered this problem while creating some fractal images. The solution to the limitation is usage of dithering. This article describes the problem and presents a simple solution.

Mausr is a library and web interface that performs unicode symbols recognition from hand drawn input using simple neural network. The symbol recognition library is written from scratch without any ML library and it implements back-propagation learning algorithm as well as basic non-linear optimization algorithms such as gradient descent and iRprop.

I spent summer of 2014 as an intern at the NVIDIA. That was quite different experience than the last year in the Google. This article describes all the aspects of being an intern in the Silicon Valley including tips how to prepare for such adventure. A big part of the summer was a road trip from Indiana to California and back and I will talk about it as well. After I returned everybody keep asking me: What is better, NVIDIA or Google? You can find out my personal opinion in the post!

Mamex is a Mandelbrot set rendering library written in C# and supports arbitrary precision (provided by GMP) for infinite zoom. The explorer can visualize Mandelbrot and Julia sets and has many additional features such as interactive color gradient editor, projections support, and batch rendering. Custom anti-aliasing algorithm, sharpening, and color dithering algorithms yields beautiful results.

In the summer of 2013 I had an opportunity to be a part of the Google for whole 14 weeks. This article tells the whole story starting from the application process describing all my great experience. I was interning at Google Headquarters in sunny California and I was member of Google Research team. This article is accompanied with around 100 images from Google campus and surrounding areas.

This project demonstrates visualization techniques like glyphs, stream lines, stream tubes, and stream surfaces, all done in real time. The key is RK4 integrator implemented using CUDA that is uses very fast texture lookup functions to access a vector field. This article contains more than 100 images and figures, commented code snippets, and source code available for download.

This project compares performance of CPU and GPU in evaluation of famous Conway's Game of Life. The performance was tested on three different implementations. The most sophisticated version of the algorithm on GPU stores data in one bit-per-cell array and leads to speed-up of 480x compared to serial CPU algorithm. The best implementation for CPU turned out to be lookup-table approach leading to 60x speedups over serial CPU. The report contains detailed explanation of used algorithms, measurements, and code of whole project for download.

Comparison of performance of CPU and GPU implementations of random faults algorithm for random terrain generation. Speedup of GPU over CPU is over 700x. Project uses shared VBO's to avoid CPU-GPU data transfer which makes it an interactive experience.

Maraytr is a ray-tracer written with high focus on algorithms and data structures rather than on performance. I decided to make it to get deeper understanding of theory and math behind ray-tracing. Also, ray-tracing is fun! The core was written in four days in C# without any third-party libraries. The scene is represented as Constructive Solid Geometry (CSG) and supported primitives are sphere, cube, and plane. It is possible to do basic boolean operations like union, intersection, subtraction, or xor.

Video of simulation of growth of simple trees restricted by environment created using L-systems. This animation was made to demonstrate power of my L-system framework Malsys and to have fun with L-systems. Whole simulation is one L-system with sub-L-systems for leaves and blooms.

Malsys is an L-system processing library with web interface and interactive gallery. Malsys supports advanced L-system features like context rewriting or parametric L-systems as well as some unique features like rewriting symbol as another L-system. This project was done as my bachelors thesis at Charles university in Prague

This project is relatively advanced L-system library written in Haskell. Out of the box it supports symbols with parameters, conditional rewriting, and it can evaluate expressions with binary and unary operators. There are two available L-system interpreters: text and SVG vector graphics. The code is well commented and written with extensibility in mind. It is easy to add new operators, new interpreters, or even extend the grammar. This project was my final program of Non-procedural programming class.

Wandering is a generic maze generator, solver, and game playable in a console. It supports hexagonal and rectangular mazes and two types of maze generators. Cool thing is that the maze type is independent of the solver. Every solver can solve every type of maze. It is possible to define new maze types, generators, and solvers. Another cool feature is the UI system in a console including menus, text boxes, windows, and screen manager. This was my first larger program written in C++.

Animation of growing tree made using L-systems. Animation starts as a small tree branching only to the right and then start turning left revealing beautiful structure. Basic rules of the tree are based on Pythagoras tree however resulting tree is not pure Pythagoras tree. This animation was made as homework to the computer graphics class.

Proof of concept of a bridge-builder game for Android made as part of Game Development course. The game written in Java supports building bridge struts and simulating physics with Box2D engine and uses AndEngine for rendering. A nice touch is parallax background.

Library and interface for automatic music sheet recognition. Input is image of sheet of music and output is standard MIDI file. Uses database of symbols together with dynamic recognition to do the recognition. This was my final project of High school and I won 'A little Czech head' prize for it.

Big poster (4 x 1.7 m) of 4 deep zooms into Mandelbrot set. I made this poster because I was amazed by Mandelbrot set and I had a program (Mandelbrot set explorer) to generate high quality images. My dad helped me to print this big guy and later I donated it to the institution where I was having programming courses after school as a kid. It is there till now.