A while back while taking a technical writing class and simultaneously working at my current job at Electroimpact, I was presented with an opportunity to draft a short whitepaper on some more innovative 3D Transformation math I was working on. While I only finished what amounted to a technical summary at the time (Since my implementations and statistical evidence were and are proprietary to EI), I figured I would share that initial paper here, and I hope that someday soon I can finish up the whitepaper and share the implementation on here.

The goal in working through this math was to find the optimal method of transforming an IMPERFECT (measured) ‘actual’ group of points onto a perfect (from design CAD) ‘nominal’ group of points. I apologize for the odd formatting, that was a requirement for initial submission of the whitepaper.

Abstract:

There are often real-world scenarios where one will have to find a point’s inferred location relative to a set of points, and are only left with imperfect points correlating to the needed point group; this paper sets out to solve this problem. This question is frequent asked in relation to computer graphics as well as the science of metrology. In order to solve this problem, we must understand the different ways to represent a point’s relationship to a point cloud, in numeric, vector, and matrix form. Additionally it is important to know how to relate point clouds to one another and find the relationship so we can transform the given point. Finally, and with the most difficulty, we need to find this relationship for an imperfect and differing set of points. We do this through either the Kabsch Algorithm of the Iterative Closest Point Algorithm.

Background Note: In order to properly understand this paper, the reader is expected to have a working knowledge of trigonometry, vector geometry, and linear algebra. While not necessary, a basic understanding of integral calculus would be helpful. No prior information on this specific topic is needed.

Otimal Transformations between Matching Point Groups

Hey There!

Welcome to my ‘blog’.

It may be interesting. It may not.

This is a place for me to ramble, post my work, share art, and otherwise bare my soul. This will likely consist of my thoughts on Math, Physics, Code, Music, and Visual Art.

I know its not much of an intro, but hey, I’m an engineer and artist, not so much an author.

 

~NGL