How to Calculate Rotation of Points Between Two 3D Points?

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Discussion Overview

The discussion revolves around calculating the rotation of multiple points in 3D space between two defined points, specifically focusing on how to derive a formula that accommodates the rotation of these points based on their proximity to two reference points. The context includes practical applications in 3D software, particularly Autodesk Maya, and involves mathematical reasoning related to vector operations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks a formula to calculate the rotation of multiple red points based on the rotation of two green points, emphasizing the need for a method that accounts for the number of red points and their relative positions.
  • Another participant suggests that the middle red point can be calculated as the average of the two green points, proposing that the other red points could be determined using a weighted average of the middle red point's rotation and the nearest green point's rotation.
  • A later reply notes the limitation of the 3D application’s math nodes, indicating that while an average node is available, a weighted average node is not, which may complicate the implementation of the proposed solution.
  • One participant asserts that it is possible to compute a weighted average using basic operations like addition, multiplication, and division, suggesting a potential workaround for the limitations mentioned.

Areas of Agreement / Disagreement

Participants generally agree on the approach to calculating the middle red point as the average of the two green points. However, there is uncertainty regarding the implementation of a weighted average due to the limitations of the software being used, and no consensus is reached on a definitive method for calculating the rotations of the other red points.

Contextual Notes

The discussion highlights limitations related to the available mathematical operations in Autodesk Maya, which may restrict the ability to perform certain calculations necessary for the proposed solutions.

simchris111
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I'm working with 3D applications, and I'm trying to figure out how to calculate the rotation of x number of points between two points.

I've made a video to illustrate what I mean:
https://www.youtube.com/watch?v=CmIk8I8itrQ

So the thing is, I need to find some kind of formula that calculates the rotation of the red points based on the rotation of the green ones. The middle red point should always be 50% between the top and the low point, but the red points below and above the middle should bias the rotation towards their closest green point. In this case I have 5 red points, it would be awesome if the formula also worked on more points.


So the formula has to work only from knowing the number of red points, and the rotation of the upper and lower green point.


I'm sorry if this is stupidly simple, but I can't seem to wrap my head around it.
 
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The middle red point seems to be just the average of the two green points, so that's easy. As for the other red points, unless there's some complexity I'm missing, you could probably just take them to be the weighted average of the rotation of the middle red point and the nearest green point; the weight will determine how biased it is towards the green point.
 
Number Nine said:
The middle red point seems to be just the average of the two green points, so that's easy. As for the other red points, unless there's some complexity I'm missing, you could probably just take them to be the weighted average of the rotation of the middle red point and the nearest green point; the weight will determine how biased it is towards the green point.
Thanks for your reply :)

That could work, however I'm limited to my 3D-application's native math-nodes (Autodesk Maya), and it doesn't seem to have a node that can do a weighted average operation. It has an average node, but not a weighted average node.

I'm sorry I forgot to say that in the first post, the math-functionality I can use is limited to these:
Plus, Minus, Avarage, Multiply, Divide, Power, Compose Matrix, Decompose Matrix, Transpose Matrix, Inverse Matrix, Vector Product
 
If you can add, multiply and divide, you can compute a weighted average.
 

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