Delaunay_circumcircles.png by Nü es CC BY-SA 3.0, via Wikimedia Commons

## Description

I'm researching surface reconstruction from point clouds using machine learning. The approach using geodesic distances gives interesting results but has some issues. The issues are mostly due to triangulation which need to be either improved or avoided.

## Tasks

Improve triangulation of patches or find ways to avoid the triangulation. Evaluate the quality of the resulting triangulations.

- Some of these:
- Triangulate patches of point clouds so that overlapping patches are consistent. Maybe proof that it always works.
- Triangulate in high-dimensional space.
- Deterministic mapping of high-dimensional points onto 2D.
- Train a neural network that converts geodesic distances and points to triangles.
- Improve sparse distance matrices.

- Metrics to evaluate the triangulations:
- Minimum angle
- Delaunay condition
- Area variance

Details for these very specific tasks will be given in the kick-off meeting.

## Requirements

- Knowledge of English language (source code comments and final report should be in English)
- Knowledge of geometry for computer graphics (e.g. surface definition with vertices and faces)
- Basic knowledge of modeling and geometry processing
- Bonus:
- Basic knowledge of Python
- Experience with C++

## Environment

The source code is currently pure Python for both Windows and Linux. C++ might be necessary for performance optimization.

## Contact

For more information please contact Philipp Erler (perler@cg.tuwien.ac.at).