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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


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





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.

$$|q_r| = 1$$



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