If you ever need more precision than what 15 decimal digits of the double format can offer, 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. With no heap allocation and no dependencies, this puts it perf-wise almost exactly halfway between a double and an arbitrary-precision library. This post explains how the format works and the math behind it. It also benchmarks the type against __float128 and 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.

The majority of our devices today can display 16.7 million colors. This may sound like a lot but sometimes the 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 the 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 a simple neural network. The symbol recognition library is written from scratch without any ML library and it implements a back-propagation learning algorithm as well as basic non-linear optimization algorithms such as gradient descent and iRprop.

I spent the summer of 2014 as an intern at NVIDIA. That was a quite different experience than the last year in Google. This article describes all the aspects of being an intern in Silicon Valley including tips how to prepare for such an 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 keeps 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 an interactive color gradient editor, projections support, and batch rendering. Custom anti-aliasing algorithm, sharpening, and color dithering algorithms yield beautiful results.

In the summer of 2013 I had an opportunity to be a part of Google for a 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 a member of the 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 an RK4 integrator implemented using CUDA that 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 a speed-up of 480x compared to the serial CPU algorithm. The best implementation for CPU turned out to be a lookup-table approach leading to 60x speedups over serial CPU. The report contains a detailed explanation of used algorithms, measurements, and code of the 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 VBOs 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 a deeper understanding of the 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 an environment created using L-systems. This animation was made to demonstrate the power of my L-system framework Malsys and to have fun with L-systems. The whole simulation is one L-system with sub-L-systems for leaves and blooms.

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

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

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

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

Big poster (4 x 1.7 m) of 4 deep zooms into the Mandelbrot set. I made this poster because I was amazed by the 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.