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Geometric Algebra - 3D Rotations and Rotors
Mathoma
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Advanced. Deep dive for people who know the field.
25K views9 years ago1 recommendation
Computer scienceGraphics and audioMath for programmersRendering
An explanation of 3D rotations and rotors using geometric algebra and reflections.
In this video, we employ the fact that two reflections is a rotation to perform rotations in 3D. We also will derive the general rotation formula, show how to compose rotations, and introduce the rotor version of this formula and discover the rotor's sign flip under a 2pi rotation. References / Further Reading: 1. Lasenby and Doran's "Geometric Algebra for Physicists". Note: This video builds off prior videos in this series, particularly: 1. Fundamentals in 2D: youtube.com/watch?v=PNlgMPzj-7Q 2. Vector Projection and Reflection: youtube.com/watch?v=ERpcSJzX448 3. Two Reflections is a Rotation: youtube.com/watch?v=Hy2gbdbrJZ8 4. Fundamentals in 3D: youtube.com/watch?v=ElLl6gzNbFE Erratum: - the sine function is odd, not even.Why it's here
1 person recommends thisWhat people say. Recommended as a quick introduction to geometric algebra for developers working with 3D linear algebra libraries.