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# System prepended metadata

title: System Solver node

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# System Solver node
Problem:
There point cloud. Each point have some vector to move.
Now, each point should have way to say if it movement vector should be limited. And that limitation is based on other points and its vectors (limited in the same way).

## Correct solution:
A system of linear (or more complex equations) is a constraints set. Each variable is a vetcor or float value. Due to the quantitative solution according to the Newton method, this can be approximated to the most optimal form.

- [Wikipedia: Newton's method](https://en.wikipedia.org/wiki/Newton%27s_method)
- [Newton’s method based collision avoidance in a CAD environment on ball nut grinding](https://link.springer.com/article/10.1007/s00170-015-7796-5)

## Cannot be applied:
- Arbitrary (non-mathematical) operations on attributes (sampling, comparison, switching, random, ...)
- There is no ready-made system that allows you to find the derivative for fields and apply it.

## Our solution:
Field task. Need to be able to set a lot of fields that can be calculated in a virtual context:
- Substep
- Random state of other vectors

### If try the described algorithm:
1. Move one vertex.
1. Check all other vertices and their constraints.
1. Move another vertex...