PPT-The Quaternions:

An Algebraic Approach 1 i j k 1 i j k 1 1 i j k 1 i j k i i 1 k j i 1 k j j j k 1 i j k 1 i k k j i 1 k j i 1 1 1 i j. P Horn Copyright 57513 2001 A quaternion can be conveniently thought of as either i a vector with four components or ii a scalar plus a vector with three components or iii a complex number with three different imaginary parts Here are three quaternio Euler Theorem + Quaternions . Representing a Point 3D. A three-dimensional point. . A. is a reference coordinate system here. Rotation along the . Z axis. In general:. Using Rotation Matrices. 靜宜大學資工系. 蔡奇偉副教授. 2010. 大綱. History of . Quaternions. Definition of Quaternion. Operations. Unit Quaternion. Operation Rules. Quaternion Transforms. Matrix Conversion. History of . 750. Texture. , Microstructure & Anisotropy. A.D. (Tony) Rollett,. . S. R. Wilson. Rodrigues. . vectors. ,. unit . Quaternions. Last revised: . 2. nd. Jan. 2015. Briefly describe rotations/orientations. The Phoenix Bird of Mathematics. Herb Klitzner. June 1, 2015. Presentation to:. New York Academy of Sciences, Lyceum Society. © 2015, Herb Klitzner. http://quaternions.klitzner.org. . The Phoenix Bird. This means, that we can represent an orientation with 3 numbers. Assuming we limit ourselves to 3 rotations without successive rotations about the same axis:. Example. Gimbal Lock. Gimbal Lock Animation. What we are going to cover. Intro to Unity. Physics & Game Objects. Cameras & Lighting. Textures & Materials. Quaternions and Rotation. Vector3’s & Coordinates. Intro to JavaScript. The Phoenix Bird of Mathematics. Herb Klitzner. June 1, . 2015. Presentation to:. New York Academy of Sciences, Lyceum . Society. © 2015, Herb Klitzner. The Phoenix Bird. CONTENTS. INTRODUCTION . APPLICATIONS. QUATERNIONS. Spring 2015. Dr. Michael J. Reale. INTRODUCTION. Quaternions invented by Sir William Rowan Hamilton in 1843. Developed as extension to complex numbers. Introduced into computer graphics by Ken Shoemake in 1985. Rollett. 27-750 . Texture, Microstructure & Anisotropy. Crystallographic orientation representations. -- Euler Angles. -. - Axis-. Angle. . -- Rodrigues-Frank Vectors. -- Unit Quaternions. A Beginners - Quaternions What They Are, How They Work, and How to Use Them for 3D Character Hierarchies Ben Kenwright School of Computing Science, Newcastle University Newcastle Upon Tyne, United Ki Determination . I. Fall . 2015. Professor Brandon A. Jones. Lecture 40: Elements of Attitude Estimation. Exam . 3 . In. -class Students: Due December 11 by 5pm. CAETE Students: Due 11. :. 59pm (Mountain) on 12/13. Lecture 4, Part B:. Orientation Representation. 1. Rotation Representation. 2. We saw that for computer graphics/games, the three most commonly used transforms are: . translation. , . rotation. . and . A.D. (Tony) Rollett,. . S. R. Wilson. Rodrigues. . vectors. ,. unit . Quaternions. Last revised: . 2. nd. Jan. 2015. Briefly describe rotations/orientations. Introduce Rodrigues-Frank vectors. Introduce .