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14parameter #1

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14 changes: 9 additions & 5 deletions doc/main.tex
Original file line number Diff line number Diff line change
Expand Up @@ -10,8 +10,8 @@
\newcommand{\matr}[1]{\mathbf{#1}}

\title{On the Chaining of Helmert transformations}
\author{Kristian Evers}
\date{2022-04-22}
\author{Kristian Evers \& Lars Stenseng}
\date{2022-08-10}

\begin{document}
\maketitle
Expand Down Expand Up @@ -132,9 +132,13 @@ \section{Chaing transformations}
\ref{eq:t3}, \ref{eq:c3} and \ref{eq:r3} and then using them in eq.
\ref{eq:simplehelmert}.

Shown here is only the 7-parameter version of the Helmert transformation
but of course this obviously also extends to the 14-parameter version and
combinations of the two.
\section{Including velocity}
Following the notation above we introduce the input, $V_A$ and output $V_B$ velocity vectors and the translation rate vector $\dot{T}$, rotation rate matrix $\dot{\matr{R}}$, and the scale rate factor $\dot{c}$.


\begin{equation}
V_B = V_A + \dot{T} + \dot{c} \dot{\matr{R}} P_A
\end{equation}


\end{document}
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