<p>You could try <a href="https://en.wikipedia.org/wiki/Natural_neighbor_interpolation" rel="nofollow noreferrer">natural neighbour interpolation</a> or Sibson coordinates for this. These coordinates are based on a Voronoi tessellation of the points.
The coordinates have been extended to an approach where the points lie on some surface in <a href="https://ac.els-cdn.com/S0925772101000189/1-s2.0-S0925772101000189-main.pdf?_tid=160000a8-d02d-11e7-99c0-00000aab0f27&amp;acdnat=1511427960_98dcfd5f9afa172805cda3bdc267f6ab" rel="nofollow noreferrer">this</a> publication.</p>

CC BY-SA 3.0
2017-11-23T09:12:09.580Z
2017-11-24T15:09:23.990Z
2017-11-24T15:09:23.990Z
Reynolds
<p>Let's assume that we have some set of points in 3d space sampled from some arbitrary surface, without self intersections and mostly flat. Is it possible to get any parametrization over this set of points?  And if it is - how?</p>

<p>My first idea was to find a plane (Maybe through PCA), or more sophisticated smooth surface which approximate this set of points, project each of these points on this fitted plane/surface and get corresponding parameters. But maybe there is better solutions for this problem.</p>

<p>Thanks for any help.</p>

CC BY-SA 3.0
2016-04-19T14:04:13.627Z
some type of [linear regression](https://en.wikipedia.org/wiki/Linear_regression) would help find the parameters
ratchet freak
<algorithm><geometry>
Parametrize set of unordered points in 3d space
Ibraim Ganiev
# Parametrize set of unordered points in 3d space

(Asked by: username_0 on 2016-04-19)

Let's assume that we have some set of points in 3d space sampled from some arbitrary surface, without self intersections and mostly flat. Is it possible to get any parametrization over this set of points? And if it is - how?

My first idea was to find a plane (Maybe through PCA), or more sophisticated smooth surface which approximate this set of points, project each of these points on this fitted plane/surface and get corresponding parameters. But maybe there is better solutions for this problem.

Thanks for any help.

**Tags:** algorithm, geometry

> **Comments:**
> **username_1**: some type of [linear regression](https://en.wikipedia.org/wiki/Linear_regression) would help find the parameters  

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## 1 answers

### Answer by username_2 on 2017-11-23. Score: 2

You could try [natural neighbour interpolation](https://en.wikipedia.org/wiki/Natural_neighbor_interpolation) or Sibson coordinates for this. These coordinates are based on a Voronoi tessellation of the points.
The coordinates have been extended to an approach where the points lie on some surface in [this](https://ac.els-cdn.com/S0925772101000189/1-s2.0-S0925772101000189-main.pdf?_tid=160000a8-d02d-11e7-99c0-00000aab0f27&acdnat=1511427960_98dcfd5f9afa172805cda3bdc267f6ab) publication.


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