PPT-Rotation of Objects about a Single Axis

Module 7 Session Topics Object Rotations Right Hand Rule Rotation Notation Single Rotation Multiple Rotations Equivalent Rotations Object Transformations Rotation A rotation is a turning of an object about a straight line known as the axis of rotation. Module 8. Session Topics. Rotations about Two Axes. Order . of Rotations. Equivalent . Rotations. Review: Rotation of Objects. Rotation: turning an object about a straight line (axis of rotation). Rotation About Two Axes. 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. 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. Lecture 5: Introduction to 3D. Recap. 2D Transformation. Generalized Transformation. Composite Transformation. OpenGL routines for 2D transformation. Objective. After completing this lecture the students will be able to. Rigid Transformations. 3D Rigid Objects. Rigid Transformation in 2D. q = (. t. x. ,t. y. ,. q. ) . with . q. . . [0,2. p. ). Robot R. 0. . R. 2. given in reference frame T. 0. What’s the new robot . Chapter 10. Copyright © 2014 John Wiley & Sons, Inc. All rights reserved.. Goals for Chapter . 10. To describe rotation in terms of:. angular. coordinates . (. q. ) . angular. velocity . (. w. KH Wong. Rotation avergaing v.6.1a. 1. Overview. What is rotation averaging?. Why we study rotation averaging?. Define the problem and formulations. What are the metric, and cost function?. What are the measurement methods: L1, L2. Module 8. HigherEdServices.org. Session Topics. Rotations about Two Axes. Order of Rotations. Equivalent Rotations. Computer Module. Review: Rotation of Objects. Rotation: turning an object about a straight line (axis of rotation). A. ngles Calculation. Lei Zhou and . Xiaolin. Li. . . October . 28, 2014. Outline . Joint Coordinate System (JCS). Concept. Example. Euler’s Angle. Helical Method. Rollett. 27-750 . Texture, Microstructure & Anisotropy. Crystallographic orientation representations. -- Euler Angles. -. - Axis-. Angle. . -- Rodrigues-Frank Vectors. -- Unit Quaternions. Module 7. Session Topics. Object Rotations. Right Hand Rule. Rotation Notation. Single Rotation. Multiple Rotations. Equivalent Rotations. Computer Module. Object Rotation. A rotation is a turning of an object about a straight line known as the axis of rotation.. 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 . Rigid Transformations. 3D Rigid Objects. Rigid Transformation in 2D. q = (. t. x. ,t. y. ,. q. ) . with . q. . . [0,2. p. ). Robot R. 0. . R. 2. given in reference frame T. 0. What’s the new robot . 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.