What does a quaternion represent?

What does a quaternion represent?

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis.

What is the conjugate of a quaternion?

Conjugate. The conjugate of a quaternion number is a quaternion with the same magnitudes but with the sign of the imaginary parts changed, so: conj(a + b i + c j + d k) = a – b i – c j – d k.

What is a quaternion in the Bible?

noun. a group or set of four persons or things. Bookbinding. four gathered sheets folded in two for binding together.

How many is 4 quaternion?

a group or set of four persons or things.

When do you use quaternions for spatial rotation?

When used to represent an orientation (rotation relative to a reference coordinate system), they are called orientation quaternions or attitude quaternions. The equation for spatial rotations can be summarized for θ radians about a unit axis as the Quaternion where and .

How are quaternions used in the real world?

Specifically, they encode information about an axis-angle rotation about an arbitrary axis. 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.

How are quaternions carried into a 3 dimensional space?

Mathematically, this operation carries the set of all “pure” quaternions p (those with real part equal to zero)—which constitute a 3-dimensional space among the quaternions—into itself, by the desired rotation about the axis u, by the angle θ. (Each real quaternion is carried into itself by this operation.

Which is the vector part of a quaternion?

The vector part of the resulting quaternion is the desired vector p′ . Mathematically, this operation carries the set of all “pure” quaternions p (those with real part equal to zero)—which constitute a 3-dimensional space among the quaternions—into itself, by the desired rotation about the axis u, by the angle θ.