![]() A reflection is an example of a transformation that takes a shape (called the preimage) and flips it across a line (called the line of reflection) to create a new shape (called the image). When used to represent an orientation (rotation relative to a reference coordinate system), they are called orientation quaternions or attitude quaternions. In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. It can describe, for example, the motion of a rigid body around a fixed point. ![]() When used to represent rotation, unit quaternions are also called rotation quaternions as they represent the 3D rotation group. Any rotation is a motion of a certain space that preserves at least one point. Rotation and orientation quaternions have applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites, and crystallographic texture analysis. Rotation is turning an object clockwise (negative) or counterclockwise (positive) about. The given point can be anywhere in the plane, even on the given object. Specifically, they encode information about an axis-angle rotation about an arbitrary axis. Rotation is one of four geometric transformations, which also include reflection, translation, and dilation. A rotation in geometry moves a given object around a given point at a given angle. Rotations may be clockwise or counterclockwise. Answer Button navigates to signup page 5 comments Comment on Alisa Zhupanenkos post Why is positive counter-c. A point can be rotated by 180 degrees, either clockwise or counterclockwise, with respect to the origin (0, 0). A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point. The mapping in the rotation is from line to line, segment to segment, and angle to angle. When rotated with respect to the origin, which acts as the reference point, the angle formed between the before and after rotation is 180 degrees. The pre-image and images have some interesting properties of rotation. An object and its rotation are the same shape and size, but the figures may be turned in different directions. A 180-degree rotation transforms a point or figure so that they are horizontally flipped. Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. A rotation is a transformation that turns a figure about a fixed point called the center of rotation. Correspondence between quaternions and 3D rotations
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