news.volyx.in

Let's remove quaternions from every 3D engine (2018) (marctenbosch.com)

627 points by lelf · 2446 days ago · 326 comments on HN

Article summary

The article discusses the potential benefits of using geometric algebra and rotors instead of quaternions for 3D rotations in graphics programming. It argues that rotors can be more intuitive and easier to understand, as they operate fully in 3D space and can be visualized without needing to resort to 4D concepts. The article also explains the basics of geometric algebra and how it can be used to represent rotations in a more natural and geometric way. This approach can lead to a deeper understanding of the underlying mathematics and potentially simplify certain calculations.

Main themes

  • Geometric Algebra
  • Quaternions
  • 3D Rotations
  • Mathematical Intuition
  • Visualization
  • Dimensionality
  • Generality of Geometric Algebra
  • Teaching and Understanding of Quaternions and Rotors
  • Practical Applications and Benefits

What commenters say

  • Some commenters argue that quaternions are already well-understood and that switching to rotors would not provide significant benefits.
  • Others believe that rotors offer a more intuitive and geometric way of thinking about 3D rotations, making them easier to understand and work with.
  • The use of geometric algebra can provide a more unified and general framework for handling rotations in any dimension, not just 3D.
  • Some argue that the choice between quaternions and rotors ultimately comes down to personal preference and the specific needs of the project.
  • The visualization of 3D rotations is not necessarily limited by the dimensionality of the representation, and other factors such as the quality of the visualization tools and the user's understanding of the mathematics can be more important.
  • Geometric algebra can be seen as a more general and powerful tool that can handle not just rotations, but also other geometric transformations and operations.
  • The complexity of quaternions is not necessarily a result of their inherent nature, but rather a consequence of the way they are typically presented and taught.
  • The potential benefits of using geometric algebra and rotors include improved understanding, simplified calculations, and increased flexibility in handling high-dimensional spaces.