# Module: tfg.geometry.transformation.dual_quaternion

This module implements TensorFlow dual quaternion utility functions.

A dual quaternion is an extension of a quaternion with the real and dual parts and written as

$$q = q_r + epsilon q_d$$

, where

$$epsilon$$

is the dual number with the property

$$e^2 = 0$$

. It can thus be represented as two quaternions, and thus stored as 8 numbers. We define the operations in terms of the two quaternions

$$q_r$$

and

$$q_d$$

.

Dual quaternions are extensions of quaternions to represent rigid transformations (rotations and translations). They are in particular important for deforming geometries as linear blending is a very close approximation of closest path blending, which is not the case for any other representation.

$$|q_r| = 1$$

.

## Functions

conjugate(...): Computes the conjugate of a dual quaternion.