From e31a1ea5384e056962ba51a634c05205cad0d15a Mon Sep 17 00:00:00 2001 From: Alexander Fabisch Date: Fri, 25 Oct 2024 09:41:42 +0200 Subject: [PATCH] Abbreviate dual quaternion symbol --- doc/source/user_guide/introduction.rst | 2 +- doc/source/user_guide/transformations.rst | 5 +++-- 2 files changed, 4 insertions(+), 3 deletions(-) diff --git a/doc/source/user_guide/introduction.rst b/doc/source/user_guide/introduction.rst index 3666239d..cb3348af 100644 --- a/doc/source/user_guide/introduction.rst +++ b/doc/source/user_guide/introduction.rst @@ -149,7 +149,7 @@ representations on the following pages. | :math:`(\pmb{p}, \pmb{q})` | | | | +----------------------------------------+---------------------+------------------+---------------+ | Dual quaternion | (8,) | X | X | -| :math:`\pmb{p} + \epsilon\pmb{q}` | | | | +| :math:`\boldsymbol{\sigma}` | | | | +----------------------------------------+---------------------+------------------+---------------+ ---------- diff --git a/doc/source/user_guide/transformations.rst b/doc/source/user_guide/transformations.rst index 41db7ab5..f8ef96a0 100644 --- a/doc/source/user_guide/transformations.rst +++ b/doc/source/user_guide/transformations.rst @@ -59,7 +59,7 @@ another representation. The following table is an overview. | :math:`(\pmb{p}, \pmb{q})` | | | | | | +----------------------------------------+------------+--------------------------+---------------+---------------+-----------------+ | Dual quaternion | Quaternion | Yes | Yes | ScLERP | Required | -| :math:`\pmb{p} + \epsilon \pmb{q}` | Conjugate | | | | | +| :math:`\boldsymbol{\sigma}` | Conjugate | | | | | +----------------------------------------+------------+--------------------------+---------------+---------------+-----------------+ --------------------- @@ -323,7 +323,8 @@ A dual quaternion consists of a real quaternion and a dual quaternion: .. math:: - \boldsymbol{p} + \epsilon \boldsymbol{q} = p_w + p_x i + p_y j + p_z k + \epsilon (q_w + q_x i + q_y j + q_z k), + \boldsymbol{\sigma} = \boldsymbol{p} + \epsilon \boldsymbol{q} + = p_w + p_x i + p_y j + p_z k + \epsilon (q_w + q_x i + q_y j + q_z k), where :math:`\epsilon^2 = 0` and :math:`\epsilon \neq 0`. We use unit dual quaternions to represent