# Embedded Delaunay triangulations for point clouds of surfaces in $\mathbb{R}^3$

## TL;DR

This paper explores conditions under which the diagonal switch algorithm can produce embedded Delaunay triangulations for point clouds on surfaces in three-dimensional space, contributing to geometric processing methods.

## Contribution

It provides sufficient conditions ensuring the diagonal switch algorithm yields embedded Delaunay triangulations for surface point clouds.

## Key findings

- Diagonal switch algorithm converges under certain conditions
- Conditions for embedding are explicitly characterized
- Enhances understanding of surface triangulation in 3D

## Abstract

In the following article we discuss Delaunay triangulations for a point cloud on an embedded surface in $\mathbb{R}^3$. We give sufficient conditions on the point cloud to show that the diagonal switch algorithm finds an embedded Delaunay triangulation.