Overview
- Pivot transformation
- Jacobian as PDF
Properties
- Analytic sampling
- Cap-preserving
- Analytic cap integrals
\begin{align}
{\color{red}\mathscr{C}}
\mapsto
{\color{green}\mathscr{C}}
&=
g({\color{red}\mathscr{C}}; {\color{RoyalBlue}\mathbf{r}_p})
\end{align}
\begin{align}
\Rightarrow
{\color{red}\mathscr{C}}
&=
g({\color{green}\mathscr{C}}; {\color{RoyalBlue}\mathbf{r}_p})
\end{align}
$\int_{\color{red}\mathscr{C}_1 \bigcap \mathscr{C}_2} D_\textrm{std}({\color{red}\boldsymbol{\omega}}) \, d {\color{red}\boldsymbol{\omega}}$
$\int_{\color{green}\mathscr{C}_1 \bigcap \mathscr{C}_2} D ({\color{green}\boldsymbol{\omega}}; {\color{RoyalBlue}\mathbf{r}_p}) \, d {\color{green}\boldsymbol{\omega}}$