Fundamentals of Quaternions for 3D Rotation and Applications
Fundamentals of Quaternions for 3D Rotation and Applications
Published 8/2025
Duration: 2h 24m | .MP4 1280x720 30 fps(r) | AAC, 44100 Hz, 2ch | 729.47 MB
Genre: eLearning | Language: English
Published 8/2025
Duration: 2h 24m | .MP4 1280x720 30 fps(r) | AAC, 44100 Hz, 2ch | 729.47 MB
Genre: eLearning | Language: English
A Practical Guide to Quaternions: From Algebra to Rotation Applications
What you'll learn
- Master the fundamentals of quaternion algebra
- Apply quaternions to perform 3D rotations
- Utilize quaternion exponentials
- Derive and implement the Rodrigues' Rotation Formula
- Connect quaternions to the principles of linear algebra
- Develop hands-on skills
- Learn power of MAPLE in handling Quaternion equations
Requirements
- High School Level Mathematics
- Conceptual Understanding of 3D Space
- Basics of Vector Calculus and Linear Algebra
Description
This course provides a comprehensive and hands-on framework for understanding and applyingquaternions, an indispensable mathematical tool for representing 3D rotations in modern technology. Over five focused sections and a total of 2.5 hours of video lectures, you will move from the foundational principles of quaternion algebra to advanced, practical applications. We'll start by demystifying the core concepts, exploring the unique properties and algebra of quaternions, and immediately connecting them to their primary purpose: controlling 2D and 3D rotations.
As the course progresses, we will answer the critical question ofwhyquaternions are a superior choice for rotation, especially for avoiding the pitfalls of other methods like gimbal lock. We will then introduce the powerful concept of quaternion exponentials and demonstrate their use in real-world scenarios, such as the familiar trackball. The bootcamp also dedicates significant time to a cornerstone of 3D rotational mechanics: the Rodrigues' Rotation Formula. You'll learn to apply this formula using quaternions to achieve precise rotations around any arbitrary axis.
Finally, we will bridge the gap between quaternion theory and the more widely known field oflinear algebra. You will learn how to express quaternion multiplication in matrix form, connecting these two powerful mathematical frameworks. Through hands-on exercises with a MAPLE worksheet, you will solidify your understanding of these relationships and gain practical experience applying both the Rodrigues' formula and other key identities. By the end of this course, you will not only understand quaternions but will also have the confidence to apply them in fields like game development, robotics, and aerospace engineering.
Who this course is for:
- Computer Graphics and Animation Specialists
- Robotics and Mechatronics Engineers
- Aerospace & Mechanical Engineers
- Game Developers & 3D Artists
- Virtual and Augmented Reality (VR/AR) Developers
- Students and Researchers
More Info