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Quasycrystal Cut-and-Project Visualization


Visualization of point sets and possible edges between them (defined from an LLL basis)

Implemented examples:

  • Ammann-Beenker QC with vertex star patterns. [Runs on GPU] (See Baake-Grimm "Aperiodic Order" p275)
  • Penrose Pointset. [Runs on CPU] (See Marlof-Strömbergsson p9)


Penrose Pointset Penrose Edges Penrose Pointset Sheared

Instructions for building from Source for Linux, Mac, Windows:

Building uses cmake and git to receive the source. Dependencies (via kipod) are GLM, GLFW and GLEW, and are installed via a package manager (on Mac/Linux) or can be cloned as submodules ( git clone --recursive )


Step 1:

Install necessary packages:

~$ sudo apt install build-essential libgl1-mesa-dev cmake git 
~$ sudo apt install libglfw3-dev glew-utils libglm-dev libglew-dev

Step 2:

Clone and Building Instruction:

~$ git clone
~$ cd quacry
~$ git clone
~$ git clone external_libs/quickhull/
~$ mkdir build
~$ cd build
~$ cmake ..
~$ make
~$ ./quacry

(If you use 'git clone --recursive', then cloning kipod and quickhull is not necessary).

MacOS (Intel/ARM)

Step 1

Install homebrew ( and xcode command line developer tools:

~$ xcode-select --install
~$ /bin/bash -c "$(curl -fsSL"

Step 2

Then install cmake, git and the necessary libraries glew, glfw3, glm:

~$ brew install git cmake glew glfw3 glm

Step 3:

See Step 2 Ubuntu.

Windows (Visual Studio 2019)

Step 1

Get git e.g. via The required libraries are included as git submodules. Use the tag --recursive to add these when cloning:

~$ git clone --recursive

Step 2

It is convenient to use the Visual Studio 2019 "C++ CMake tools for Windows" component. It is already installed with the "Desktop development with C++" and "Linux Development with C++" workload. Opening the folder will detect the cmake file automatically.


Quasicrystal visualization via cut and project construction.







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