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<title>Graphics/Gloss/Data/QuadTree.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE RankNTypes #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-comment'>-- | A QuadTree can be used to recursively divide up 2D space into quadrants.</span>
<a name="line-4"></a><span class='hs-comment'>--   The smallest division corresponds to an unit `Extent`, so the total depth </span>
<a name="line-5"></a><span class='hs-comment'>--   of the tree will depend on what sized `Extent` you start with.</span>
<a name="line-6"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Graphics</span><span class='hs-varop'>.</span><span class='hs-conid'>Gloss</span><span class='hs-varop'>.</span><span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>QuadTree</span>
<a name="line-7"></a>	<span class='hs-layout'>(</span> <span class='hs-conid'>QuadTree</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-8"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>emptyTree</span>
<a name="line-9"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>emptyNode</span>
<a name="line-10"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>takeQuadOfTree</span>
<a name="line-11"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>liftToQuad</span>
<a name="line-12"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>insertByPath</span>
<a name="line-13"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>insertByCoord</span>
<a name="line-14"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>lookupNodeByPath</span>
<a name="line-15"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>lookupByPath</span>
<a name="line-16"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>lookupByCoord</span>
<a name="line-17"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>flattenQuadTree</span>
<a name="line-18"></a>	<span class='hs-layout'>,</span> <span class='hs-varid'>flattenQuadTreeWithExtents</span><span class='hs-layout'>)</span>
<a name="line-19"></a><span class='hs-keyword'>where</span>
<a name="line-20"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Graphics</span><span class='hs-varop'>.</span><span class='hs-conid'>Gloss</span><span class='hs-varop'>.</span><span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Quad</span>
<a name="line-21"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Graphics</span><span class='hs-varop'>.</span><span class='hs-conid'>Gloss</span><span class='hs-varop'>.</span><span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Extent</span>
<a name="line-22"></a>
<a name="line-23"></a><a name="QuadTree"></a><span class='hs-comment'>-- | The quad tree structure.</span>
<a name="line-24"></a><a name="QuadTree"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span>
<a name="line-25"></a>	<span class='hs-comment'>-- | An empty node.</span>
<a name="line-26"></a>	<span class='hs-keyglyph'>=</span> <span class='hs-conid'>TNil</span>
<a name="line-27"></a>
<a name="line-28"></a>	<span class='hs-comment'>-- | A leaf containint some value.</span>
<a name="line-29"></a>	<span class='hs-keyglyph'>|</span> <span class='hs-conid'>TLeaf</span> <span class='hs-varid'>a</span>
<a name="line-30"></a>	
<a name="line-31"></a>	<span class='hs-comment'>-- | A node with four children.</span>
<a name="line-32"></a>	<span class='hs-keyglyph'>|</span> <span class='hs-conid'>TNode</span> <span class='hs-layout'>(</span><span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> 	<span class='hs-comment'>-- NW NE</span>
<a name="line-33"></a>		<span class='hs-layout'>(</span><span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>	<span class='hs-comment'>-- SW SE</span>
<a name="line-34"></a>	<span class='hs-keyword'>deriving</span> <span class='hs-conid'>Show</span>
<a name="line-35"></a>
<a name="line-36"></a>
<a name="line-37"></a><a name="emptyTree"></a><span class='hs-comment'>-- | A `TNil` tree.</span>
<a name="line-38"></a><span class='hs-definition'>emptyTree</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span>
<a name="line-39"></a><span class='hs-definition'>emptyTree</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>TNil</span>
<a name="line-40"></a>
<a name="line-41"></a>
<a name="line-42"></a><a name="emptyNode"></a><span class='hs-comment'>-- | A node with `TNil`. for all its branches.</span>
<a name="line-43"></a><span class='hs-definition'>emptyNode</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span>
<a name="line-44"></a><span class='hs-definition'>emptyNode</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>TNode</span> <span class='hs-conid'>TNil</span> <span class='hs-conid'>TNil</span> <span class='hs-conid'>TNil</span> <span class='hs-conid'>TNil</span>
<a name="line-45"></a>
<a name="line-46"></a>
<a name="line-47"></a><a name="takeQuadOfTree"></a><span class='hs-comment'>-- | Get a quadrant from a node.</span>
<a name="line-48"></a><span class='hs-comment'>--   If the tree does not have an outer node then `Nothing`.</span>
<a name="line-49"></a><span class='hs-definition'>takeQuadOfTree</span>
<a name="line-50"></a>	<span class='hs-keyglyph'>::</span> <span class='hs-conid'>Quad</span>
<a name="line-51"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span>
<a name="line-52"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-53"></a>
<a name="line-54"></a><span class='hs-definition'>takeQuadOfTree</span> <span class='hs-varid'>quad</span> <span class='hs-varid'>tree</span>
<a name="line-55"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>tree</span> <span class='hs-keyword'>of</span>
<a name="line-56"></a>	<span class='hs-conid'>TNil</span>		<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Nothing</span>
<a name="line-57"></a>	<span class='hs-conid'>TLeaf</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span>		<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Nothing</span>
<a name="line-58"></a>	<span class='hs-conid'>TNode</span> <span class='hs-varid'>nw</span> <span class='hs-varid'>ne</span> <span class='hs-varid'>sw</span> <span class='hs-varid'>se</span>
<a name="line-59"></a>	 <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>quad</span> <span class='hs-keyword'>of</span>
<a name="line-60"></a>		<span class='hs-conid'>NW</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>nw</span>
<a name="line-61"></a>		<span class='hs-conid'>NE</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>ne</span>
<a name="line-62"></a>		<span class='hs-conid'>SW</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>sw</span>
<a name="line-63"></a>		<span class='hs-conid'>SE</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>se</span>
<a name="line-64"></a>
<a name="line-65"></a>
<a name="line-66"></a><a name="liftToQuad"></a><span class='hs-comment'>-- | Apply a function to a quadrant of a node.</span>
<a name="line-67"></a><span class='hs-comment'>--   If the tree does not have an outer node then return the original tree.</span>
<a name="line-68"></a><span class='hs-definition'>liftToQuad</span>
<a name="line-69"></a>	<span class='hs-keyglyph'>::</span> <span class='hs-conid'>Quad</span>
<a name="line-70"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> 
<a name="line-71"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span>  <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span>
<a name="line-72"></a>
<a name="line-73"></a><span class='hs-definition'>liftToQuad</span> <span class='hs-varid'>quad</span> <span class='hs-varid'>f</span> <span class='hs-varid'>tree</span>
<a name="line-74"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>tree</span> <span class='hs-keyword'>of</span>
<a name="line-75"></a>	<span class='hs-conid'>TNil</span>		<span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>tree</span>
<a name="line-76"></a>	<span class='hs-conid'>TLeaf</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span>		<span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>tree</span>
<a name="line-77"></a>	<span class='hs-conid'>TNode</span> <span class='hs-varid'>nw</span> <span class='hs-varid'>ne</span> <span class='hs-varid'>sw</span> <span class='hs-varid'>se</span>
<a name="line-78"></a>	 <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>quad</span> <span class='hs-keyword'>of</span>
<a name="line-79"></a>		<span class='hs-conid'>NW</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>TNode</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>nw</span><span class='hs-layout'>)</span> <span class='hs-varid'>ne</span> <span class='hs-varid'>sw</span> <span class='hs-varid'>se</span>
<a name="line-80"></a>		<span class='hs-conid'>NE</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>TNode</span> <span class='hs-varid'>nw</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>ne</span><span class='hs-layout'>)</span> <span class='hs-varid'>sw</span> <span class='hs-varid'>se</span>
<a name="line-81"></a>		<span class='hs-conid'>SW</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>TNode</span> <span class='hs-varid'>nw</span> <span class='hs-varid'>ne</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>sw</span><span class='hs-layout'>)</span> <span class='hs-varid'>se</span>
<a name="line-82"></a>		<span class='hs-conid'>SE</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>TNode</span> <span class='hs-varid'>nw</span> <span class='hs-varid'>ne</span> <span class='hs-varid'>sw</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>se</span><span class='hs-layout'>)</span>
<a name="line-83"></a>		 
<a name="line-84"></a>		
<a name="line-85"></a><a name="insertByPath"></a><span class='hs-comment'>-- | Insert a value into the tree at the position given by a path.</span>
<a name="line-86"></a><span class='hs-comment'>--   If the path intersects an existing `TLeaf` then return the original tree.</span>
<a name="line-87"></a><span class='hs-definition'>insertByPath</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Quad</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span>
<a name="line-88"></a>	
<a name="line-89"></a><span class='hs-definition'>insertByPath</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>x</span> <span class='hs-keyword'>_</span>
<a name="line-90"></a>	<span class='hs-keyglyph'>=</span> <span class='hs-conid'>TLeaf</span> <span class='hs-varid'>x</span>
<a name="line-91"></a>	
<a name="line-92"></a><span class='hs-definition'>insertByPath</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span><span class='hs-conop'>:</span><span class='hs-varid'>qs</span><span class='hs-layout'>)</span> <span class='hs-varid'>x</span> <span class='hs-varid'>tree</span>
<a name="line-93"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>tree</span> <span class='hs-keyword'>of</span>
<a name="line-94"></a>	<span class='hs-conid'>TNil</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>liftToQuad</span> <span class='hs-varid'>q</span> <span class='hs-layout'>(</span><span class='hs-varid'>insertByPath</span> <span class='hs-varid'>qs</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>emptyNode</span>
<a name="line-95"></a>	<span class='hs-conid'>TLeaf</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>tree</span>
<a name="line-96"></a>	<span class='hs-conid'>TNode</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>liftToQuad</span> <span class='hs-varid'>q</span> <span class='hs-layout'>(</span><span class='hs-varid'>insertByPath</span> <span class='hs-varid'>qs</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varid'>tree</span>
<a name="line-97"></a>
<a name="line-98"></a>
<a name="line-99"></a><a name="insertByCoord"></a><span class='hs-comment'>-- | Insert a value into the node containing this coordinate.</span>
<a name="line-100"></a><span class='hs-comment'>--   The node is created at maximum depth, corresponding to an unit `Extent`.</span>
<a name="line-101"></a><span class='hs-definition'>insertByCoord</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Extent</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Coord</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-102"></a><span class='hs-definition'>insertByCoord</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>coord</span> <span class='hs-varid'>x</span> <span class='hs-varid'>tree</span>
<a name="line-103"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>	<span class='hs-varid'>path</span>	<span class='hs-keyglyph'>&lt;-</span> <span class='hs-varid'>pathToCoord</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>coord</span>
<a name="line-104"></a>	<span class='hs-varid'>return</span>	<span class='hs-varop'>$</span>  <span class='hs-varid'>insertByPath</span> <span class='hs-varid'>path</span> <span class='hs-varid'>x</span> <span class='hs-varid'>tree</span>
<a name="line-105"></a>
<a name="line-106"></a>
<a name="line-107"></a><a name="lookupNodeByPath"></a><span class='hs-comment'>-- | Lookup a node based on a path to it.</span>
<a name="line-108"></a><span class='hs-definition'>lookupNodeByPath</span>
<a name="line-109"></a>	<span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Quad</span><span class='hs-keyglyph'>]</span>
<a name="line-110"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span>
<a name="line-111"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span>
<a name="line-112"></a>
<a name="line-113"></a><span class='hs-definition'>lookupNodeByPath</span> <span class='hs-conid'>[]</span> <span class='hs-varid'>tree</span>
<a name="line-114"></a>	<span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>tree</span>
<a name="line-115"></a>	
<a name="line-116"></a><span class='hs-definition'>lookupNodeByPath</span> <span class='hs-layout'>(</span><span class='hs-varid'>q</span><span class='hs-conop'>:</span><span class='hs-varid'>qs</span><span class='hs-layout'>)</span> <span class='hs-varid'>tree</span>
<a name="line-117"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>tree</span> <span class='hs-keyword'>of</span>
<a name="line-118"></a>	<span class='hs-conid'>TNil</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Nothing</span>
<a name="line-119"></a>	<span class='hs-conid'>TLeaf</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Nothing</span>
<a name="line-120"></a>	<span class='hs-conid'>TNode</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span>
<a name="line-121"></a>	 <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyword'>let</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>quad</span>	<span class='hs-keyglyph'>=</span> <span class='hs-varid'>takeQuadOfTree</span> <span class='hs-varid'>q</span> <span class='hs-varid'>tree</span>
<a name="line-122"></a>	    <span class='hs-keyword'>in</span>  <span class='hs-varid'>lookupNodeByPath</span> <span class='hs-varid'>qs</span> <span class='hs-varid'>quad</span>
<a name="line-123"></a>
<a name="line-124"></a>
<a name="line-125"></a><a name="lookupByPath"></a><span class='hs-comment'>-- | Lookup an element based given a path to it.</span>
<a name="line-126"></a><span class='hs-definition'>lookupByPath</span> <span class='hs-keyglyph'>::</span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Quad</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span>
<a name="line-127"></a><span class='hs-definition'>lookupByPath</span> <span class='hs-varid'>path</span> <span class='hs-varid'>tree</span>
<a name="line-128"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>lookupNodeByPath</span> <span class='hs-varid'>path</span> <span class='hs-varid'>tree</span> <span class='hs-keyword'>of</span>
<a name="line-129"></a>	<span class='hs-conid'>Just</span> <span class='hs-layout'>(</span><span class='hs-conid'>TLeaf</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>x</span>
<a name="line-130"></a>	<span class='hs-keyword'>_</span>		<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Nothing</span>
<a name="line-131"></a>
<a name="line-132"></a>
<a name="line-133"></a><a name="lookupByCoord"></a><span class='hs-comment'>-- | Lookup a node if a tree given a coordinate which it contains.</span>
<a name="line-134"></a><span class='hs-definition'>lookupByCoord</span> 
<a name="line-135"></a>	<span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span>
<a name="line-136"></a>	<span class='hs-varop'>.</span>  <span class='hs-conid'>Extent</span> 	<span class='hs-comment'>-- ^ Extent that covers the whole tree.</span>
<a name="line-137"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Coord</span> 	<span class='hs-comment'>-- ^ Coordinate of the value of interest.</span>
<a name="line-138"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span> 
<a name="line-139"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>a</span>
<a name="line-140"></a><span class='hs-definition'>lookupByCoord</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>coord</span> <span class='hs-varid'>tree</span>
<a name="line-141"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>do</span>	<span class='hs-varid'>path</span>	<span class='hs-keyglyph'>&lt;-</span> <span class='hs-varid'>pathToCoord</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>coord</span>
<a name="line-142"></a>	<span class='hs-varid'>lookupByPath</span> <span class='hs-varid'>path</span> <span class='hs-varid'>tree</span>
<a name="line-143"></a>	
<a name="line-144"></a>	
<a name="line-145"></a><a name="flattenQuadTree"></a><span class='hs-comment'>-- | Flatten a QuadTree into a list of its contained values, with coordinates.</span>
<a name="line-146"></a><span class='hs-definition'>flattenQuadTree</span> 
<a name="line-147"></a>	<span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span>
<a name="line-148"></a>	<span class='hs-varop'>.</span>  <span class='hs-conid'>Extent</span> 	<span class='hs-comment'>-- ^ Extent that covers the whole tree.</span>
<a name="line-149"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span> 
<a name="line-150"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-conid'>Coord</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-151"></a>	
<a name="line-152"></a><span class='hs-definition'>flattenQuadTree</span> <span class='hs-varid'>extentInit</span> <span class='hs-varid'>treeInit</span>
<a name="line-153"></a> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>flatten'</span> <span class='hs-varid'>extentInit</span> <span class='hs-varid'>treeInit</span>
<a name="line-154"></a> <span class='hs-keyword'>where</span>	<span class='hs-varid'>flatten'</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>tree</span>
<a name="line-155"></a> 	 <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>tree</span> <span class='hs-keyword'>of</span>
<a name="line-156"></a>		<span class='hs-conid'>TNil</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>[]</span>
<a name="line-157"></a>		<span class='hs-conid'>TLeaf</span> <span class='hs-varid'>x</span>	
<a name="line-158"></a>		 <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyword'>let</span> <span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span> <span class='hs-varid'>s</span><span class='hs-layout'>,</span> <span class='hs-keyword'>_</span><span class='hs-layout'>,</span> <span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>takeExtent</span> <span class='hs-varid'>extent</span>
<a name="line-159"></a>		    <span class='hs-keyword'>in</span>  <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>w</span><span class='hs-layout'>,</span> <span class='hs-varid'>s</span><span class='hs-layout'>)</span><span class='hs-layout'>,</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-160"></a>
<a name="line-161"></a>		<span class='hs-conid'>TNode</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>concat</span> <span class='hs-varop'>$</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>flattenQuad</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>tree</span><span class='hs-layout'>)</span> <span class='hs-varid'>allQuads</span>
<a name="line-162"></a>			
<a name="line-163"></a>	<span class='hs-varid'>flattenQuad</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>tree</span> <span class='hs-varid'>quad</span>
<a name="line-164"></a> 	 <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span>	<span class='hs-varid'>extent'</span>		<span class='hs-keyglyph'>=</span> <span class='hs-varid'>cutQuadOfExtent</span> <span class='hs-varid'>quad</span> <span class='hs-varid'>extent</span>
<a name="line-165"></a>		<span class='hs-conid'>Just</span> <span class='hs-varid'>tree'</span>	<span class='hs-keyglyph'>=</span> <span class='hs-varid'>takeQuadOfTree</span> <span class='hs-varid'>quad</span> <span class='hs-varid'>tree</span>
<a name="line-166"></a>   	   <span class='hs-keyword'>in</span>	<span class='hs-varid'>flatten'</span> <span class='hs-varid'>extent'</span> <span class='hs-varid'>tree'</span>
<a name="line-167"></a>
<a name="line-168"></a>
<a name="line-169"></a><a name="flattenQuadTreeWithExtents"></a><span class='hs-comment'>-- | Flatten a QuadTree into a list of its contained values, with coordinates.</span>
<a name="line-170"></a><span class='hs-definition'>flattenQuadTreeWithExtents</span>
<a name="line-171"></a>	<span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span>
<a name="line-172"></a>	<span class='hs-varop'>.</span>  <span class='hs-conid'>Extent</span> 	<span class='hs-comment'>-- ^ Extent that covers the whole tree.</span>
<a name="line-173"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span> 
<a name="line-174"></a>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-conid'>Extent</span><span class='hs-layout'>,</span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-175"></a>	
<a name="line-176"></a><span class='hs-definition'>flattenQuadTreeWithExtents</span> <span class='hs-varid'>extentInit</span> <span class='hs-varid'>treeInit</span>
<a name="line-177"></a> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>flatten'</span> <span class='hs-varid'>extentInit</span> <span class='hs-varid'>treeInit</span>
<a name="line-178"></a> <span class='hs-keyword'>where</span>	<span class='hs-varid'>flatten'</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>tree</span>
<a name="line-179"></a> 	 <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>tree</span> <span class='hs-keyword'>of</span>
<a name="line-180"></a>		<span class='hs-conid'>TNil</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>[]</span>
<a name="line-181"></a>		<span class='hs-conid'>TLeaf</span> <span class='hs-varid'>x</span>	
<a name="line-182"></a>		 <span class='hs-keyglyph'>-&gt;</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>extent</span><span class='hs-layout'>,</span> <span class='hs-varid'>x</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span>
<a name="line-183"></a>
<a name="line-184"></a>		<span class='hs-conid'>TNode</span><span class='hs-layout'>{</span><span class='hs-layout'>}</span>	<span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>concat</span> <span class='hs-varop'>$</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-varid'>flattenQuad</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>tree</span><span class='hs-layout'>)</span> <span class='hs-varid'>allQuads</span>
<a name="line-185"></a>			
<a name="line-186"></a>	<span class='hs-varid'>flattenQuad</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>tree</span> <span class='hs-varid'>quad</span>
<a name="line-187"></a> 	 <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span>	<span class='hs-varid'>extent'</span>		<span class='hs-keyglyph'>=</span> <span class='hs-varid'>cutQuadOfExtent</span> <span class='hs-varid'>quad</span> <span class='hs-varid'>extent</span>
<a name="line-188"></a>		<span class='hs-conid'>Just</span> <span class='hs-varid'>tree'</span>	<span class='hs-keyglyph'>=</span> <span class='hs-varid'>takeQuadOfTree</span> <span class='hs-varid'>quad</span> <span class='hs-varid'>tree</span>
<a name="line-189"></a>   	   <span class='hs-keyword'>in</span>	<span class='hs-varid'>flatten'</span> <span class='hs-varid'>extent'</span> <span class='hs-varid'>tree'</span>
<a name="line-190"></a>
<a name="line-191"></a>
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