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<title>Data/Graph/Inductive/Query/GVD.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>-- (c) 2000-2005 by Martin Erwig [see file COPYRIGHT]</span>
<a name="line-2"></a><span class='hs-comment'>-- | Graph Voronoi Diagram </span>
<a name="line-3"></a>
<a name="line-4"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span><span class='hs-varop'>.</span><span class='hs-conid'>Inductive</span><span class='hs-varop'>.</span><span class='hs-conid'>Query</span><span class='hs-varop'>.</span><span class='hs-conid'>GVD</span> <span class='hs-layout'>(</span>
<a name="line-5"></a> <span class='hs-conid'>Voronoi</span><span class='hs-layout'>,</span>
<a name="line-6"></a> <span class='hs-varid'>gvdIn</span><span class='hs-layout'>,</span><span class='hs-varid'>gvdOut</span><span class='hs-layout'>,</span>
<a name="line-7"></a> <span class='hs-varid'>voronoiSet</span><span class='hs-layout'>,</span><span class='hs-varid'>nearestNode</span><span class='hs-layout'>,</span><span class='hs-varid'>nearestDist</span><span class='hs-layout'>,</span><span class='hs-varid'>nearestPath</span><span class='hs-layout'>,</span>
<a name="line-8"></a><span class='hs-comment'>-- vd,nn,ns,</span>
<a name="line-9"></a><span class='hs-comment'>-- vdO,nnO,nsO</span>
<a name="line-10"></a><span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-11"></a>
<a name="line-12"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-varid'>listToMaybe</span><span class='hs-layout'>)</span>
<a name="line-13"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>List</span> <span class='hs-layout'>(</span><span class='hs-varid'>nub</span><span class='hs-layout'>)</span>
<a name="line-14"></a>
<a name="line-15"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span><span class='hs-varop'>.</span><span class='hs-conid'>Inductive</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>Heap</span> <span class='hs-keyword'>as</span> <span class='hs-conid'>H</span>
<a name="line-16"></a>
<a name="line-17"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span><span class='hs-varop'>.</span><span class='hs-conid'>Inductive</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span>
<a name="line-18"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span><span class='hs-varop'>.</span><span class='hs-conid'>Inductive</span><span class='hs-varop'>.</span><span class='hs-conid'>Query</span><span class='hs-varop'>.</span><span class='hs-conid'>SP</span> <span class='hs-layout'>(</span><span class='hs-varid'>dijkstra</span><span class='hs-layout'>)</span>
<a name="line-19"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span><span class='hs-varop'>.</span><span class='hs-conid'>Inductive</span><span class='hs-varop'>.</span><span class='hs-conid'>Internal</span><span class='hs-varop'>.</span><span class='hs-conid'>RootPath</span>
<a name="line-20"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Graph</span><span class='hs-varop'>.</span><span class='hs-conid'>Inductive</span><span class='hs-varop'>.</span><span class='hs-conid'>Basic</span>
<a name="line-21"></a>
<a name="line-22"></a><a name="Voronoi"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Voronoi</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LRTree</span> <span class='hs-varid'>a</span>
<a name="line-23"></a>
<a name="line-24"></a><a name="gvdIn"></a><span class='hs-definition'>gvdIn</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>DynGraph</span> <span class='hs-varid'>gr</span><span class='hs-layout'>,</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Node</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>gr</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Voronoi</span> <span class='hs-varid'>b</span>
<a name="line-25"></a><span class='hs-definition'>gvdIn</span> <span class='hs-varid'>vs</span> <span class='hs-varid'>g</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>gvdOut</span> <span class='hs-varid'>vs</span> <span class='hs-layout'>(</span><span class='hs-varid'>grev</span> <span class='hs-varid'>g</span><span class='hs-layout'>)</span>
<a name="line-26"></a>
<a name="line-27"></a><a name="gvdOut"></a><span class='hs-definition'>gvdOut</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Graph</span> <span class='hs-varid'>gr</span><span class='hs-layout'>,</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=></span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Node</span><span class='hs-keyglyph'>]</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>gr</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Voronoi</span> <span class='hs-varid'>b</span>
<a name="line-28"></a><span class='hs-definition'>gvdOut</span> <span class='hs-varid'>vs</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>dijkstra</span> <span class='hs-layout'>(</span><span class='hs-conid'>H</span><span class='hs-varop'>.</span><span class='hs-varid'>build</span> <span class='hs-layout'>(</span><span class='hs-varid'>zip</span> <span class='hs-layout'>(</span><span class='hs-varid'>repeat</span> <span class='hs-num'>0</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>v</span><span class='hs-keyglyph'>-></span><span class='hs-conid'>LP</span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>v</span><span class='hs-layout'>,</span><span class='hs-num'>0</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>]</span><span class='hs-layout'>)</span> <span class='hs-varid'>vs</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-29"></a>
<a name="line-30"></a><a name="voronoiSet"></a><span class='hs-definition'>voronoiSet</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Node</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Voronoi</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-conid'>Node</span><span class='hs-keyglyph'>]</span>
<a name="line-31"></a><span class='hs-definition'>voronoiSet</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>nub</span> <span class='hs-varop'>.</span> <span class='hs-varid'>concat</span> <span class='hs-varop'>.</span> <span class='hs-varid'>filter</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-varid'>p</span><span class='hs-keyglyph'>-></span><span class='hs-varid'>last</span> <span class='hs-varid'>p</span><span class='hs-varop'>==</span><span class='hs-varid'>v</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>map</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>LP</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>-></span><span class='hs-varid'>map</span> <span class='hs-varid'>fst</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span>
<a name="line-32"></a>
<a name="line-33"></a><a name="maybePath"></a><span class='hs-definition'>maybePath</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Node</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Voronoi</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>LPath</span> <span class='hs-varid'>b</span><span class='hs-layout'>)</span>
<a name="line-34"></a><span class='hs-definition'>maybePath</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>listToMaybe</span> <span class='hs-varop'>.</span> <span class='hs-varid'>filter</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>LP</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-keyword'>_</span><span class='hs-layout'>)</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>-></span><span class='hs-varid'>w</span><span class='hs-varop'>==</span><span class='hs-varid'>v</span><span class='hs-layout'>)</span>
<a name="line-35"></a>
<a name="line-36"></a><a name="nearestNode"></a><span class='hs-definition'>nearestNode</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Node</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Voronoi</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-conid'>Node</span>
<a name="line-37"></a><span class='hs-definition'>nearestNode</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>LP</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-keyword'>_</span><span class='hs-layout'>)</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>-></span><span class='hs-varid'>w</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>maybePath</span> <span class='hs-varid'>v</span>
<a name="line-38"></a>
<a name="line-39"></a><a name="nearestDist"></a><span class='hs-definition'>nearestDist</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Node</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Voronoi</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-varid'>b</span>
<a name="line-40"></a><span class='hs-definition'>nearestDist</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>LP</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-layout'>,</span><span class='hs-varid'>l</span><span class='hs-layout'>)</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>-></span><span class='hs-varid'>l</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>maybePath</span> <span class='hs-varid'>v</span>
<a name="line-41"></a>
<a name="line-42"></a><a name="nearestPath"></a><span class='hs-definition'>nearestPath</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Real</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>=></span> <span class='hs-conid'>Node</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Voronoi</span> <span class='hs-varid'>b</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-conid'>Path</span>
<a name="line-43"></a><span class='hs-definition'>nearestPath</span> <span class='hs-varid'>v</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>fmap</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-conid'>LP</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span><span class='hs-keyglyph'>-></span><span class='hs-varid'>map</span> <span class='hs-varid'>fst</span> <span class='hs-varid'>p</span><span class='hs-layout'>)</span> <span class='hs-varop'>.</span> <span class='hs-varid'>maybePath</span> <span class='hs-varid'>v</span>
<a name="line-44"></a>
<a name="line-45"></a>
<a name="line-46"></a><span class='hs-comment'>-- vd = gvdIn [4,5] vor</span>
<a name="line-47"></a><span class='hs-comment'>-- vdO = gvdOut [4,5] vor</span>
<a name="line-48"></a><span class='hs-comment'>-- nn = map (flip nearestNode vd) [1..8]</span>
<a name="line-49"></a><span class='hs-comment'>-- nnO = map (flip nearestNode vdO) [1..8]</span>
<a name="line-50"></a><span class='hs-comment'>-- ns = map (flip voronoiSet vd) [1..8]</span>
<a name="line-51"></a><span class='hs-comment'>-- nsO = map (flip voronoiSet vdO) [1..8]</span>
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