# 3D Rotations

1.1 3D ROTATIONS As mentioned in Preface, 3D rotation has been historically an important theme of physics in relation to rigid body motion and quantum mechanics. In today's computer age, however, “computational” aspects of 3D rotation ...

Author: Kenichi Kanatani

Publisher: CRC Press

ISBN: 9781000070668

Category: Computers

Page: 157

View: 221

3D rotation analysis is widely encountered in everyday problems thanks to the development of computers. Sensing 3D using cameras and sensors, analyzing and modeling 3D for computer vision and computer graphics, and controlling and simulating robot motion all require 3D rotation computation. This book focuses on the computational analysis of 3D rotation, rather than classical motion analysis. It regards noise as random variables and models their probability distributions. It also pursues statistically optimal computation for maximizing the expected accuracy, as is typical of nonlinear optimization. All concepts are illustrated using computer vision applications as examples. Mathematically, the set of all 3D rotations forms a group denoted by SO(3). Exploiting this group property, we obtain an optimal solution analytical or numerically, depending on the problem. Our numerical scheme, which we call the "Lie algebra method," is based on the Lie group structure of SO(3). This book also proposes computing projects for readers who want to code the theories presented in this book, describing necessary 3D simulation setting as well as providing real GPS 3D measurement data. To help readers not very familiar with abstract mathematics, a brief overview of quaternion algebra, matrix analysis, Lie groups, and Lie algebras is provided as Appendix at the end of the volume.
Categories: Computers

# 3D Math Primer for Graphics and Game Development

His name is also attached to Euler's rotation theorem, which basically says that any 3D angular displacement can be ... With Euler angles, we need three rotations to describe any orientation, since we are restricted to rotate about the ...

Author: Fletcher Dunn

Publisher: CRC Press

ISBN: 9781498759892

Category: Computers

Page: 846

View: 103

This engaging book presents the essential mathematics needed to describe, simulate, and render a 3D world. Reflecting both academic and in-the-trenches practical experience, the authors teach you how to describe objects and their positions, orientations, and trajectories in 3D using mathematics. The text provides an introduction to mathematics for
Categories: Computers

# 3D Electro Rotation of Single Cells

However, it is necessary to extend the basic two-electrode structure to multiple electrodes to achieve more complex manipulations, such as single-cell rotation. In this work, a thick-electrode DEP chip for single-cell 3D rotation was ...

Author: Liang Huang

Publisher: Springer Nature

ISBN: 9783031016660

Category: Technology & Engineering

Page: 101

View: 874

Dielectrophoresis microfluidic chips have been widely used in various biological applications due to their advantages of convenient operation, high throughput, and low cost. However, most of the DEP microfluidic chips are based on 2D planar electrodes which have some limitations, such as electric field attenuation, small effective working regions, and weak DEP forces. In order to overcome the limitations of 2D planar electrodes, two kinds of thick-electrode DEP chips were designed to realize manipulation and multi-parameter measurement of single cells. Based on the multi-electrode structure of thick-electrode DEP, a single-cell 3D electro-rotation chip of "Armillary Sphere" was designed. The chip uses four thick electrodes and a bottom planar electrode to form an electric field chamber, which can control 3D rotation of single cells under different electric signal configurations. Electrical property measurement and 3D image reconstruction of single cells are achieved based on single-cell 3D rotation. This work overcomes the limitations of 2D planar electrodes and effectively solves the problem of unstable spatial position of single-cell samples, and provides a new platform for single-cell analysis. Based on multi-electrode structure of thick-electrode DEP, a microfluidic chip with optoelectronic integration was presented. A dual-fiber optical stretcher embedded in thick electrodes can trap and stretch a single cell while the thick electrodes are used for single-cell rotation. Stretching and rotation manipulation gives the chip the ability to simultaneously measure mechanical and electrical properties of single cells, providing a versatile platform for single-cell analysis, further extending the application of thick-electrode DEP in biological manipulation and analysis.
Categories: Technology & Engineering

# Rotation Transforms for Computer Graphics

In the context of a 3D rotation matrix, an eigenvector is a vector scaled by λ but not rotated, which implies that it is the axis of rotation. To illustrate this, let's identify the eigenvector for the composite rotation (9.3) above: ...

Author: John Vince

Publisher: Springer Science & Business Media

ISBN: 9780857291547

Category: Computers

Page: 232

View: 350

Rotation transforms are used everywhere in computer graphics from rotating pictures in editing software, to providing an arbitrary view of a 3D virtual environment. Although the former is a trivial operation, the latter can be a challenging task. Rotation Transforms for Computer Graphics covers a wide range of mathematical techniques used for rotating points and frames of reference in the plane and 3D space. It includes many worked examples and over 100 illustrations that make it essential reading for students, academics, researchers and professional practitioners. The book includes introductory chapters on complex numbers, matrices, quaternions and geometric algebra, and further chapters on how these techniques are employed in 2D and 3D computer graphics. In particular, matrix and bivector transforms are developed and evaluated to rotate points in a fixed frame of reference, and vice versa.
Categories: Computers

# Computer Vision ACCV 2018

(a) 3D rotation of camera (b) spherical panorama (c) projection of and projected images 3D rotation Fig. 2. Relation between 3D and 2D rotations. (a) 3D rotation (α, β) of the camera and the captured 360 panorama image.

Author: C.V. Jawahar

Publisher: Springer

ISBN: 9783030208738

Category: Computers

Page: 727

View: 183

The six volume set LNCS 11361-11366 constitutes the proceedings of the 14th Asian Conference on Computer Vision, ACCV 2018, held in Perth, Australia, in December 2018. The total of 274 contributions was carefully reviewed and selected from 979 submissions during two rounds of reviewing and improvement. The papers focus on motion and tracking, segmentation and grouping, image-based modeling, dep learning, object recognition object recognition, object detection and categorization, vision and language, video analysis and event recognition, face and gesture analysis, statistical methods and learning, performance evaluation, medical image analysis, document analysis, optimization methods, RGBD and depth camera processing, robotic vision, applications of computer vision.
Categories: Computers

# Fast Quantitative Magnetic Resonance Imaging

2.4.3 3D EULER ROTATIONS 2D trajectories can fill 3D k-space with rotated, instead of stacked, repeats of the trajectory. The complication with this method is that unlike in two dimensions, rotations in three dimensions do not commute, ...

Author: Guido Buonincontri

Publisher: Morgan & Claypool Publishers

ISBN: 9781681736952

Category: Medical

Page: 124

View: 384

Among medical imaging modalities, magnetic resonance imaging (MRI) stands out for its excellent soft-tissue contrast, anatomical detail, and high sensitivity for disease detection. However, as proven by the continuous and vast effort to develop new MRI techniques, limitations and open challenges remain. The primary source of contrast in MRI images are the various relaxation parameters associated with the nuclear magnetic resonance (NMR) phenomena upon which MRI is based. Although it is possible to quantify these relaxation parameters (qMRI) they are rarely used in the clinic, and radiological interpretation of images is primarily based upon images that are relaxation time weighted. The clinical adoption of qMRI is mainly limited by the long acquisition times required to quantify each relaxation parameter as well as questions around their accuracy and reliability. More specifically, the main limitations of qMRI methods have been the difficulty in dealing with the high inter-parameter correlations and a high sensitivity to MRI system imperfections. Recently, new methods for rapid qMRI have been proposed. The multi-parametric models at the heart of these techniques have the main advantage of accounting for the correlations between the parameters of interest as well as system imperfections. This holistic view on the MR signal makes it possible to regress many individual parameters at once, potentially with a higher accuracy. Novel, accurate techniques promise a fast estimation of relevant MRI quantities, including but not limited to longitudinal (T1) and transverse (T2) relaxation times. Among these emerging methods, MR Fingerprinting (MRF), synthetic MR (syMRI or MAGIC), and T1‒T2 Shuffling are making their way into the clinical world at a very fast pace. However, the main underlying assumptions and algorithms used are sometimes different from those found in the conventional MRI literature, and can be elusive at times. In this book, we take the opportunity to study and describe the main assumptions, theoretical background, and methods that are the basis of these emerging techniques. Quantitative transient state imaging provides an incredible, transformative opportunity for MRI. There is huge potential to further extend the physics, in conjunction with the underlying physiology, toward a better theoretical description of the underlying models, their application, and evaluation to improve the assessment of disease and treatment efficacy.
Categories: Medical

# Data Mining and Data Visualization

For triples of quantitative variables, the method of choice is 3D data rotations. Such rotations let us perceive structure among three variables as shape of point scatters in virtual 3D space. Although not obvious, three-dimensional ...

Author:

Publisher: Elsevier

ISBN: 0080459404

Category: Mathematics

Page: 800

View: 764

Data Mining and Data Visualization focuses on dealing with large-scale data, a field commonly referred to as data mining. The book is divided into three sections. The first deals with an introduction to statistical aspects of data mining and machine learning and includes applications to text analysis, computer intrusion detection, and hiding of information in digital files. The second section focuses on a variety of statistical methodologies that have proven to be effective in data mining applications. These include clustering, classification, multivariate density estimation, tree-based methods, pattern recognition, outlier detection, genetic algorithms, and dimensionality reduction. The third section focuses on data visualization and covers issues of visualization of high-dimensional data, novel graphical techniques with a focus on human factors, interactive graphics, and data visualization using virtual reality. This book represents a thorough cross section of internationally renowned thinkers who are inventing methods for dealing with a new data paradigm. Distinguished contributors who are international experts in aspects of data mining Includes data mining approaches to non-numerical data mining including text data, Internet traffic data, and geographic data Highly topical discussions reflecting current thinking on contemporary technical issues, e.g. streaming data Discusses taxonomy of dataset sizes, computational complexity, and scalability usually ignored in most discussions Thorough discussion of data visualization issues blending statistical, human factors, and computational insights
Categories: Mathematics

# Adobe After Effects CS4 Classroom in a Book

You can adjust 3D rotation two ways: by changing a layer's Orientation values, or changing its X, Y, and Z Rotation ... the layer moves along the shortest possible rotational path in 3D space, creating natural and predictable rotations.

Publisher: Peachpit Press

ISBN: 013208922X

Category: Computers

Page: 400

View: 996

Categories: Computers

# Computer Graphics Using Java 2D and 3D

A 3D shear shifts a point along a plane, and the amount of the shift depends on the distance of the point to the ... Rotation. 3D rotations are complex operations. A general 3D rotation has an axis of rotation that can be any line in ...

Author: Hong Zhang

Publisher: Prentice Hall

ISBN: 9780130351180

Category: Computers

Page: 462

View: 338

This Java handbook makes a practical tutorial on Java 2D and Java 3D for computer professionals. It contains in-depth coverage of basic computer graphics concepts and techniques, and introduces advanced graphic features to an audience mostly trained in the Java language. Chapter topics include mathematical background for computer graphics, .geometric transformation, views, lighting and texturing, behavior and interaction, and animation.For computer programmers and engineers, data analysts, graphic designers/animators, and game developers.
Categories: Computers

# Quaternion Fourier Transforms for Signal and Image Processing

3D rotations Given a 3D vector p, represented as a pure quaternion, the rotations of p in 3D space are encoded using one unit quaternion q (i.e. q ∈ H and |q| = 1) and are given by: Rq ...

Author: Todd A. Ell

Publisher: John Wiley & Sons

ISBN: 9781848214781

Category: Technology & Engineering

Page: 160

View: 437

Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book’s attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.
Categories: Technology & Engineering