Quaternion Courses and Certifications

Michael Penn

A Quaternion Version of Euler's Formula

A concise exploration of a quaternion version of Euler's formula.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

3Blue1Brown

Visualizing Quaternions - 4D Numbers With Stereographic Projection

Visualize quaternions as rotations of a four-dimensional sphere projected into three dimensions, revealing the geometry and non-commutativity of quaternion multiplication.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Geometry of the Dihedrons and Quaternions - Famous Math Problems

Explore Dihedrons, sister algebras to Quaternions, through their rich relativistic geometry, determinant quadratic form, and connections to complex numbers.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Rotation Problem and Hamilton's Discovery of Quaternions - Part 4

Practical implementation of quaternions for 3D rotations, focusing on half-turns and vector trigonometry. Explores quaternion multiplication and its geometric interpretation for rotations.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Rotation Problem and Hamilton's Discovery of Quaternions - Famous Math Problems

Develops quaternions through 2×2 complex matrices, deriving their arithmetic laws and visual representation before connecting them to rotations in three-dimensional space.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Mecharithm - Robotics and Mechatronics

Unit Quaternions in Robotics - Great Demos - Fundamentals of Robotics

Learn how unit quaternions represent robot orientations without singularities, including conversions to Euler angles, rotation matrices, and exponential coordinates.

• YouTube
• 24 minutes
• Self-Paced
• Free Video

EDUCBA

DirectX: Implement & Optimize 3D Rendering

Implement DirectX rasterizer customization, blend states and depth buffering, optimize textures with mip maps, design sampling shaders, and apply quaternions with C++/CX ref classes.

• Coursera
• 3 weeks, 3 hours a week
• Self-Paced
• Paid Course

Packt

Advanced Game Math - Affine Transformations

Apply affine transformations in games: build translation, scaling, rotation, shear and reflection matrices with homogeneous coordinates, and use quaternion rotations in Unity to avoid gimbal lock.

• Coursera
• 2 weeks, 3 hours a week
• Self-Paced
• Paid Course

Michael Penn

The Only Real Cross Product is Three-Dimensional

Explore the unique properties of 3D cross products, their mathematical significance, and why they don't exist in other dimensions. Gain insights into vector algebra and spatial geometry.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Rotation Problem and Hamilton's Discovery of Quaternions - Part 2 - Famous Math Problems 13b

Explore 3D rotations, their composition, and algebraic representation. Learn about Euler's theorem, vector operations, and the foundations for understanding quaternions in graphics and rocket science.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Ross Dynamics Lab

Quaternions for Rotation, Axis-Angle, Euler Parameters - MATLAB Examples - Rodrigues Rotation Formula

Explore axis-angle rotation and Euler parameters for rigid-body orientation, with MATLAB demonstrations converting between rotation matrices, quaternions, and angular representations.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

GDC

A Visual Guide to Quaternions and Dual Quaternions - Math in Game Development

Explore a concrete, 3D visualization of quaternions in game development. Learn creation, interpolation, and composition techniques for enhanced understanding and practical application.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Michael Penn

The Duality Between Quaternions and Vectors

Explore the fascinating relationship between quaternions and vectors, uncovering their dual nature and applications in mathematics and physics.

• YouTube
• 16 minutes
• Self-Paced
• Free Video

Freya Holmér

Why Can't You Multiply Vectors? - A Mathematical Journey into Vector Multiplication

Een wiskundige reis door vectorvermenigvuldiging, complexe getallen en geometrische algebra, met toepassingen in game-ontwikkeling en nieuwe perspectieven op wiskundige constructies.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Insights into Mathematics

Central Polynumber Algebra and Baby Weyl Character Formula - Math Foundations 236

Explores central polynumber algebra and Weyl character formula, focusing on SU(2) and SU(3) representations. Connects to particle physics and quaternions, emphasizing polynumbers over complex exponentials.

• YouTube
• 40 minutes
• Self-Paced
• Free Video