PPT-The Culture of Quaternions

The Phoenix Bird of Mathematics Herb Klitzner June 1 2015 Presentation to New York Academy of Sciences Lyceum Society 2015 Herb Klitzner httpquaternionsklitznerorg The Phoenix Bird. In sum it means cultivating and refining a thing to such an extent that its end product evokes our admiration and respect This is practically the same as Sanskriti of the Sanskrit language The term Sanskriti has been derived from the root Kri to do You have never had to bother about having to make your own script or creating a new language system for yourself These are already given to you which you enjoy as a member of society Then you build on it by making your contribution or addition which Getting Used to . American Culture. Education System. Weather. Time. Dress. Greetings. Informality. Individuality. Personal Space. Medical . Care/Insurance. Dating. Smoking. Pets. Telephone. Helping. 1. Rank 3-4 Coxeter Groups, Quaternions and . Quasicrystals. . Mehmet Koca . . Department of Physics. College of Science. Sultan Qaboos University. Muscat-OMAN. kocam@squ.edu.om. References . Polyhedra obtained from Coxeter groups and quaternions. . 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. 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. Accountability. A personal commitment to achieving the organization’s results.. See It. Own It. Solve It. Do It.. People who are habitually . Above the Line . accept they are . part of the solution.. 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 . Com S 437. What can we do with it? . Goal: Implement an algorithm to rotate an object, using the . Arcball. paradigm. Input: Mouse movement. Output: a rotation matrix for a 3D object. Demo . Let’s first see what arc ball can do before digging into the theory. 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 .