<p>If you have a fixed object with different shapes and movements, pair-wise- or multi-matching can be a helpful solution for you. For example see <a href="https://arxiv.org/pdf/1811.10541.pdf" rel="nofollow noreferrer">this paper</a>. This method can be extended for higher-dimensions as well.</p>

<blockquote>
  <p><a href="https://i.stack.imgur.com/Ndlf9.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Ndlf9.png" alt="enter image description here"></a></p>
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<p>If you have two different sets of points that come from different objects and you find the similarity between them, one solution can be computing <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.90.937&amp;rep=rep1&amp;type=pdf" rel="nofollow noreferrer">discrete Frechet distance</a> in both sets of points and then compare their value.</p>

<blockquote>
  <p><a href="https://i.stack.imgur.com/EexZp.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/EexZp.png" alt="enter image description here"></a></p>
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<p>The other related concept is <strong>Shape Reconstruction</strong>. You can mix the result of a proper shape reconstruction algorithm with two previous methods to compute the similarity:</p>

<blockquote>
  <p><a href="https://i.stack.imgur.com/Ffn6Q.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/Ffn6Q.png" alt="enter image description here"></a></p>
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How to know if two sets of points have same pattern
<p>I have 2 sets of points in 3D have the same count, I want to know if the have the same pattern, I thought I may project them on XZ,XY and YZ planes then compare the projections in each plane but I am not sure how to do this, I thought the convex hull may help but it won't be accurate.
Is there an easy algorithm to do that? the complexity is not a big issue so far as the points count will be tiny, I implement in Java.</p>

<p>Can I solve this in 3D direct with the same algorithm ?</p>

<p>The attached image shows an example of what I mean.</p>

<p>Edit:
No guarantee for order.
No scale, there are rotation and translation only.</p>

<p><a href="https://i.stack.imgur.com/EUbL4.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/EUbL4.png" alt="enter image description here"></a></p>