PPT-Quaternion

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 . LaV iola Jr Bro wn Uni ersity echnology Center for Adv anced Scienti57346c Computing and isualization PO Box 1910 Pro vidence RI 02912 USA Emailjjlcsbrownedu Abstract The unscented Kalman 57346lter is superior alter na ti to the extended Kalman 5734 with Quaternion Curves Shoemaker Singer Company Link Flight Simulation Division CT bodies roll and tumble through space. In computer animation, so do cameras. The rotations of these objects are best Open-source C++ Library Implementation. Notation and Identities. Details:. . Rotation matrices, special orthogonal group, quaternions, calculation of quaternion vector rotation, parallel, antiparallel, robust rotation matrix to quaternion conversions, and vice versa.. 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. 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. 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. Rollett. 27-750 . Texture, Microstructure & Anisotropy. Crystallographic orientation representations. -- Euler Angles. -. - Axis-. Angle. . -- Rodrigues-Frank Vectors. -- Unit Quaternions. 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. Interpolating Values. Animation(U), Chap 3, Interpolating Values. 1. 2. Outline. Interpolating/approximating curves. Controlling the motion of a point along a curve. Interpolation of orientation. Working with paths. The Camera Navigating and viewing the virtual world Camera properties and definition Perspective transformation Quaternion transforms for changing camera Road Map pinhole camera model tiny aperture finite size screen 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. Notation and Identities. Details:. . Rotation matrices, special orthogonal group, quaternions, calculation of quaternion vector rotation, parallel, antiparallel, robust rotation matrix to quaternion conversions, and vice versa.. 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 .