surf-vec-defects

Locates topological defects in tangent vector fields to a sphere

Locates topological defects in tangent vector fields to a sphere, by computing Burger circuits around each point.

The code has been developed for usage on vector fields living on a spherical surface centered at the origin, sampled on a (quasi-)regular point grid through a list of three-dimensional vectors. However, the code should be able to work on closed surfaces centered at the origin with no overhangs, for instance ellipsoids or weakly perturbed spheres.

The function DefectTrackSurf takes 2 mandatory arguments and a third optional:

- the array of points r of size (# of points)x3
- the array of sampled vectors v of size (# of points)x3x(# of time points)
- the distance dr between nearest neighbors points. If not provided, dr defaults to sin(2pi/sqrt(# grid points)), the approximate spacing between points on a regular grid on the sphere.

Please find the mathematical details of the algorithm at
https://drive.google.com/file/d/1s_5GXzcphbt8bVqCTsxOaLMuaihzjxvJ/view?usp=sharing

If you find this work useful, please

This work has been developed with valuable inputs from Alexander Mietke for analyzis of the zebrafish embryo. If you find this work useful, please cite the preprint https://arxiv.org/abs/2103.08130