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\documentclass{article}
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\title{Region layering}
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\usepackage{graphicx,amsmath}
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\section{Introduction}
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When regions overlap in time, we need to decide which one should be
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Each region on a playlist is on a \emph{layer}. All overlapping regions
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are on a unique layer, and when overlaps exist the highest-layered
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region is played. This is illustrated in Figure~\ref{fig:basic-layering}.
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\includegraphics{basic-layering.pdf}
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\caption{Basic region layering}
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\label{fig:basic-layering}
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Here we see that region $A$ overlaps $B$, $B$ overlaps $C$, and
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$D$ overlaps nothing. There are several ways in which these regions
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could be arranged; in the drawing, $A$ is on layer~2, $B$ on layer~1,
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$C$ and $D$ on layer~0. If this area is played back, region $A$ will
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play in its entirety, followed by the end part of region $B$, followed
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by the end part of region $C$, followed by the whole of region $D$.
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This follows the basic rule that, at any given point, the region on
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the highest layer will be played.
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\section{Which layer does a region go on?}
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The logic to decide which layer a region goes onto is somewhat complicated.
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This section describes it in hand-wavey and more technical terms.
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\subsection{Hand-wavey description}
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A playlist maintains an internal \emph{layering order} for regions. This order
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is not directly visible in Ardour, but it's useful to understand it
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nonetheless. Figure~\ref{fig:layering-order-1} gives a rough idea of what this
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\includegraphics{layering-order-1.pdf}
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\caption{Layering order}
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\label{fig:layering-order-1}
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Here we see 6 regions; as the layering order value increases, the region will
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be placed on a higher layer.
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Every time any region is moved, added or edited, a \emph{relayer} occurs. This
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collapses the regions down into layers. For our example, this would result in
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the arrangement in Figure~\ref{fig:layering-order-2}.
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\includegraphics{layering-order-2.pdf}
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\label{fig:layering-order-2}
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The relayer operation takes each region, in the layering order, and puts it
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on the lowest possible layer that it can be on without overlap.
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\subsubsection{Layering order}
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Given that arrangement, the remaining question is how the layering order is
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arrived at. The rules are as follows:
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\item When a region is added to a playlist, it goes above the current highest
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region in the layering order.
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\item In `overlaid' track mode, moving or editing regions does not change the
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layering order. Hence, moving regions about will maintain their position in
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the layering order. Changing overlaps may change the \emph{layer} that the
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region ends up on, but not the order in which they will be layered.
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\item In `stacked' track mode, moving regions places the region on the layer
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that they are dropped on. This is achieved by modifying the layering order
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for the region that is moved, so that when the relayer operation happens the
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region ends up on the desired layer.
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\item When regions are `raised' or `lowered' in the stack, the layering order
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is modified to achieve the desired layer change.
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The upshot of all this is that regions should maintain their expected layering
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order, unless that order is explicitly change using `stacked' mode or by
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explicit layering commands like `raise' or `lower'.
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\subsection{Technical description}
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Each region on a playlist has three layering-related properties: its current
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layer $c$ (an integer) and its layering index $i$ (also an integer). It also
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has an \emph{optional} pending layer $p$ which is fractional.
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Whenever a region is added, moved, trimmed, etc.\ we run a \emph{relayer}. This
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\item Take a list of all regions and remove those who have a value for $p$.
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\item Sort the remainder in ascending order of $i$.
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\item Insert the regions which have a value for $p$ in the correct place in the
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list by comparing $c$ of those in the list to $p$ of the inserted region.
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\item Iterate over the resulting list, putting each region on the lowest available
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layer, setting its current layer $c$, and clearing $p$.
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\item If any region had a pending layer, iterate through the region list again
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giving each region a new layering index $i$ ascending from 0.
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The pending layer $p$ is set up in the following situations:
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\item When a region is added to the playlist, $p$ is set to $\infty$.
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\item When a region is raised to the top of the playlist, $p$ is set to $\infty$.
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\item When a region is raised one step in the playlist, $p$ is set to $c + 1.5$.
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\item When a region is lowered to the bottom of the playlist, $p$ is set to $-0.5$.
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\item When a region is lowered one step int the playlist, $p$ is set to $c - 1.5$.
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\item When a region is explicitly put between layers $A$ and $B$ in `stacked'
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mode, $p$ is set to $(A + B) / 2$.
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The idea of this approach is that the layering indices $i$ are used to keep a
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current state of the stack, and this state is used to maintain region
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relationships. Setting $p$ will alter these relationships, after which the
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layering indices $i$ are updated to reflect the new status quo.
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It is not sufficient to use current layer $c$ as the state of the stack.
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Consider two overlapping regions $P$ and $Q$, with $P$ on layer~0 and $Q$ on
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layer~1. Now raise $P$ to the top of the stack, so that $Q$ is on layer~0 and
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$P$ on layer~1. Move $P$ away from $Q$ (in overlaid mode) so that both regions
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are on layer~0. Now drag $P$ back over $Q$. One would expect $P$ to return to
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the top of the stack, since it was explicitly raised earlier. However, if the
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relayer operation were to compare $c$ for each region, they would be identical;
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the information that $P$ was once higher than $Q$ has been lost.
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\section{Stacked mode}
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When a track is being displayed in \emph{stacked} mode, regions are spread out
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vertically to indicate their layering, like in Figure~\ref{fig:stacked}.
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\includegraphics[scale=0.5]{stacked.png}
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\caption{A track in stacked mode}
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In this mode, layering is performed \emph{explicitly}. In other words, the
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user's immediate actions decide which layer a region should be put on. When a
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region move drag is started in stacked mode, the regions separate further out
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vertically, to leave space between each layer, as shown in
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Figure~\ref{fig:stacked-drag}.
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\includegraphics[scale=0.5]{stacked-drag.png}
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\caption{A track in stacked mode during a drag}
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\label{fig:stacked-drag}
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The region(s) being dragged can then be dropped in any location, horizontally
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and vertically, and the regions will be layered accordingly.
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\section{Overlaid mode}
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When a track is being displayed in \emph{overlaid} mode, regions are
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displayed on top of one another, like in Figure~\ref{fig:overlaid}.
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\includegraphics[scale=0.5]{overlaid.png}
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\caption{A track in overlaid mode}
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In this mode, drags of regions maintain the same \emph{layer ordering}, even if the layers may