Digital Geometry

Digital geometry and geometric algebra

This part of my research aims at exploring digital geometry with geometric algebra. In particular, we focus on 2D bijective digitized reflections and rotations. We first studied the digitization through geometric algebra, we characterized the set of bijective digitized reflections in the plane. We derived new bijective digitized rotations as compositions of bijective digitized reflections since any rotation is represented as the composition of two reflections. We also compared them with those obtained through geometric transformations by computing their distributions.

C++ implementation

git clone https://github.com/sbreuils/GADigitizedTransformations.git

Want to know some details

The first paper is available here. This is a collaboration with Yukiko Kenmochi and Akihiro Sugimoto.

Want to cite

@inproceedings{breuils:hal-03168979,
  title = {Visiting bijective digitized reflections and rotations using geometric algebra},
  author = {Breuils, St{\'e}phane and Kenmochi, Y. and Sugimoto, Akihiro},
  url = {https://hal.archives-ouvertes.fr/hal-03168979},
  booktitle = {International Conference on Discrete Geometry and Mathematical Morphology},
  address = {Uppsala, Sweden},
  year = {2021},
  month = May
}

Slides of the beginning of the project

Here you can find the slides presented at DGMM conference DGMM in May 2021:

Stephane Breuils