quaternion -凯发k8网页登录

quaternions are vectors used for computing rotations in mechanics, aerospace, computer graphics, vision processing, and other applications. they consist of four elements: three that extend the commonly known imaginary number and one that defines the magnitude of rotation. quaternions are commonly denoted as:

\[q=w x\mathbf{i} y\mathbf{j} z\mathbf{k}\quad\text{where}\quad \mathbf{i}^2=\mathbf{j}^2=\mathbf{k}^2=\mathbf{i}\mathbf{j}\mathbf{k}=-1\]

this rotation format requires less computation than a rotation matrix.

common tasks for using quaternion include:

• converting between quaternions, rotation matrices, and direction cosine matrices
• performing quaternion math such as norm inverse and rotation
• simulating premade six degree-of freedom (6dof) models built with quaternion math

for details, see matlab^® and simulink^® that enable you to use quaternions without a deep understanding of the mathematics involved.