The Challenge of Applying Pure Mathematics to 3D Rotations
When you try to transfer the theoretical concept of simple harmonic motion to bone rotations in 3D, it's common to encounter several practical obstacles. The problem you describe is very frequent among animators who decide to explore mathematical control of their animations. While translations usually behave more predictably, rotations introduce additional complexities related to units, coordinate systems, and how the software interprets angles over time.
Understanding the Specific Problems of Rotations
The two main problems you mention -excessive speed and erratic initial behavior- have very concrete technical explanations. The fast speed generally indicates a mismatch between the time units your software uses and those you're considering in your equation, while the strange behavior in the first frames is usually due to issues with value initialization or interpretation of the initial phase.
- Incorrect time unit conversion between seconds and frames
- Problems with the evaluation order of mathematical expressions
- Incorrect handling of the initial phase in the rotation context
- Angular range limitations and value wrapping
Solutions for Correct Harmonic Motion in Rotations
To fix these problems, you need to adjust several aspects of your implementation. The key is understanding that rotations require special considerations that don't apply to translations, especially when working with script controllers.
Implementing harmonic motion in rotations is like translating poetry into another language: the essence is the same but the rules change
- Correctly convert time from frames to seconds using FPS
- Adjust the angular velocity (w) considering that in rotations the values are more sensitive
- Verify the amplitude range (a) to avoid extreme rotations
- Stabilize the initial phase (p) with values that avoid initial jumps
Recommended Parameters to Start With
If you're starting with simple harmonic motion in rotations, we recommend starting with conservative values that allow you to understand the system's behavior before scaling to more complex configurations.
Mastering simple harmonic motion in 3D animation is like learning to play a musical instrument: it requires understanding the theory but also developing a practical ear to adjust the parameters until it sounds right 🎵. Patience at this stage will reward you with more natural and controlled animations in the future.