Euler angles are a method for representing the orientation of a rigid body in three-dimensional space using three angles, which describe rotations about the axes of a coordinate system. They are widely used in fields like robotics, aerospace, and computer graphics, but can suffer from gimbal lock, a situation where the representation loses a degree of freedom.

Euler Angles

Euler angles

orientation of a rigid body

Three-dimensional space is a geometric setting in which three values, often referred to as dimensions, are required to determine the position of an element. It is the physical universe we live in, where objects have length, width, and height, allowing for the representation and manipulation of objects in a realistic manner.

three-dimensional space

describe rotations

axes of a coordinate system

Robotics is an interdisciplinary field that integrates computer science and engineering to design, construct, and operate robots, which are machines capable of performing tasks autonomously or semi-autonomously. The field aims to enhance efficiency and precision in various applications, from manufacturing and healthcare to exploration and personal assistance.

robotics

aerospace

Computer graphics is the field of computer science that focuses on generating and manipulating visual content using computational techniques. It encompasses a range of applications from video games and simulations to user interface design and virtual reality, relying on both hardware and software to render and display images efficiently.

computer graphics

Gimbal lock occurs when using Euler angles to represent 3D rotations, causing a loss of one degree of freedom as two of the rotational axes align. This can lead to unexpected behavior in systems relying on these rotations, such as in animations or aircraft control, necessitating alternative representations like quaternions to avoid the issue.

gimbal lock

Degrees of freedom refer to the number of independent values or quantities which can be assigned to a statistical distribution, without violating any given restrictions. They represent the number of independent ways a dynamic system can move without violating its constraints, thus playing a crucial role in statistical significance testing and mechanical movement analysis.

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