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<title>Graphics/Gloss/Algorithms/RayCast.hs</title>
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<pre><a name="line-1"></a><span class='hs-comment'>{-# LANGUAGE PatternGuards, RankNTypes #-}</span>
<a name="line-2"></a>
<a name="line-3"></a><span class='hs-comment'>-- | Various ray casting algorithms.</span>
<a name="line-4"></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'>Algorithms</span><span class='hs-varop'>.</span><span class='hs-conid'>RayCast</span>
<a name="line-5"></a> <span class='hs-layout'>(</span> <span class='hs-varid'>castSegIntoCellularQuadTree</span>
<a name="line-6"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>traceSegIntoCellularQuadTree</span><span class='hs-layout'>)</span>
<a name="line-7"></a><span class='hs-keyword'>where</span>
<a name="line-8"></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'>Picture</span>
<a name="line-9"></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-10"></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-11"></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'>QuadTree</span>
<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'>List</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'>Function</span>
<a name="line-14"></a>
<a name="line-15"></a>
<a name="line-16"></a><a name="castSegIntoCellularQuadTree"></a><span class='hs-comment'>-- | The quadtree contains cells of unit extent (NetHack style).</span>
<a name="line-17"></a><span class='hs-comment'>-- Given a line segement (P1-P2) through the tree, get the cell </span>
<a name="line-18"></a><span class='hs-comment'>-- closest to P1 that intersects the segment, if any.</span>
<a name="line-19"></a><span class='hs-comment'>-- </span>
<a name="line-20"></a><span class='hs-comment'>-- TODO: This currently uses a naive algorithm. It just calls </span>
<a name="line-21"></a><span class='hs-comment'>-- `traceSegIntoCellularQuadTree` and sorts the results</span>
<a name="line-22"></a><span class='hs-comment'>-- to get the one closest to P1. It'd be better to do a </span>
<a name="line-23"></a><span class='hs-comment'>-- proper walk over the tree in the direction of the ray.</span>
<a name="line-24"></a><span class='hs-comment'>-- </span>
<a name="line-25"></a><span class='hs-definition'>castSegIntoCellularQuadTree</span>
<a name="line-26"></a> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span>
<a name="line-27"></a> <span class='hs-varop'>.</span> <span class='hs-conid'>Point</span> <span class='hs-comment'>-- ^ (P1) Starting point of seg.</span>
<a name="line-28"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Point</span> <span class='hs-comment'>-- ^ (P2) Final point of seg.</span>
<a name="line-29"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Extent</span> <span class='hs-comment'>-- ^ Extent convering the whole tree.</span>
<a name="line-30"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span> <span class='hs-comment'>-- ^ The tree.</span>
<a name="line-31"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Maybe</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</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-comment'>-- ^ Intersection point, extent of cell, value of cell (if any).</span>
<a name="line-32"></a>
<a name="line-33"></a><span class='hs-definition'>castSegIntoCellularQuadTree</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>tree</span>
<a name="line-34"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>cells</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-keyword'>_</span><span class='hs-conop'>:</span><span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>traceSegIntoCellularQuadTree</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>tree</span>
<a name="line-35"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>c</span> <span class='hs-conop'>:</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'><-</span> <span class='hs-varid'>sortBy</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varid'>compareDistanceTo</span> <span class='hs-varid'>p1</span><span class='hs-layout'>)</span> <span class='hs-varop'>`on`</span> <span class='hs-layout'>(</span><span class='hs-keyglyph'>\</span><span class='hs-layout'>(</span><span class='hs-varid'>a</span><span class='hs-layout'>,</span> <span class='hs-keyword'>_</span><span class='hs-layout'>,</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>a</span><span class='hs-layout'>)</span> <span class='hs-layout'>)</span> <span class='hs-varid'>cells</span>
<a name="line-36"></a> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Just</span> <span class='hs-varid'>c</span>
<a name="line-37"></a>
<a name="line-38"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span>
<a name="line-39"></a> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Nothing</span>
<a name="line-40"></a>
<a name="line-41"></a><a name="compareDistanceTo"></a><span class='hs-definition'>compareDistanceTo</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Ordering</span>
<a name="line-42"></a><span class='hs-definition'>compareDistanceTo</span> <span class='hs-varid'>p0</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span>
<a name="line-43"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-varid'>d1</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>distance</span> <span class='hs-varid'>p0</span> <span class='hs-varid'>p1</span>
<a name="line-44"></a> <span class='hs-varid'>d2</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>distance</span> <span class='hs-varid'>p0</span> <span class='hs-varid'>p2</span>
<a name="line-45"></a> <span class='hs-keyword'>in</span> <span class='hs-varid'>compare</span> <span class='hs-varid'>d1</span> <span class='hs-varid'>d2</span>
<a name="line-46"></a>
<a name="line-47"></a><a name="distance"></a><span class='hs-definition'>distance</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Float</span>
<a name="line-48"></a><span class='hs-definition'>distance</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-layout'>,</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>x2</span><span class='hs-layout'>,</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span>
<a name="line-49"></a> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>let</span> <span class='hs-varid'>xd</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>x2</span> <span class='hs-comment'>-</span> <span class='hs-varid'>x1</span>
<a name="line-50"></a> <span class='hs-varid'>yd</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>y2</span> <span class='hs-comment'>-</span> <span class='hs-varid'>y1</span>
<a name="line-51"></a> <span class='hs-keyword'>in</span> <span class='hs-varid'>sqrt</span> <span class='hs-layout'>(</span><span class='hs-varid'>xd</span> <span class='hs-varop'>*</span> <span class='hs-varid'>xd</span> <span class='hs-varop'>+</span> <span class='hs-varid'>yd</span> <span class='hs-varop'>*</span> <span class='hs-varid'>yd</span><span class='hs-layout'>)</span>
<a name="line-52"></a>
<a name="line-53"></a>
<a name="line-54"></a><a name="traceSegIntoCellularQuadTree"></a><span class='hs-comment'>-- | The quadtree contains cells of unit extent (NetHack style).</span>
<a name="line-55"></a><span class='hs-comment'>-- Given a line segment (P1-P2) through the tree, return the list of cells </span>
<a name="line-56"></a><span class='hs-comment'>-- that intersect the segment.</span>
<a name="line-57"></a><span class='hs-comment'>-- </span>
<a name="line-58"></a><span class='hs-definition'>traceSegIntoCellularQuadTree</span>
<a name="line-59"></a> <span class='hs-keyglyph'>::</span> <span class='hs-keyword'>forall</span> <span class='hs-varid'>a</span>
<a name="line-60"></a> <span class='hs-varop'>.</span> <span class='hs-conid'>Point</span> <span class='hs-comment'>-- ^ (P1) Starting point of seg.</span>
<a name="line-61"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Point</span> <span class='hs-comment'>-- ^ (P2) Final point of seg.</span>
<a name="line-62"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>Extent</span> <span class='hs-comment'>-- ^ Extent covering the whole tree.</span>
<a name="line-63"></a> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>QuadTree</span> <span class='hs-varid'>a</span> <span class='hs-comment'>-- ^ The tree.</span>
<a name="line-64"></a> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-conid'>Point</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> <span class='hs-comment'>-- ^ Intersection point, extent of cell, value of cell.</span>
<a name="line-65"></a>
<a name="line-66"></a><span class='hs-definition'>traceSegIntoCellularQuadTree</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-varid'>extent</span> <span class='hs-varid'>tree</span>
<a name="line-67"></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-68"></a> <span class='hs-conid'>TNil</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>[]</span>
<a name="line-69"></a> <span class='hs-conid'>TLeaf</span> <span class='hs-varid'>a</span>
<a name="line-70"></a> <span class='hs-keyglyph'>-></span> <span class='hs-keyword'>case</span> <span class='hs-varid'>intersectSegExtent</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-varid'>extent</span> <span class='hs-keyword'>of</span>
<a name="line-71"></a> <span class='hs-conid'>Just</span> <span class='hs-varid'>pos</span> <span class='hs-keyglyph'>-></span> <span class='hs-keyglyph'>[</span><span class='hs-layout'>(</span><span class='hs-varid'>pos</span><span class='hs-layout'>,</span> <span class='hs-varid'>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-72"></a> <span class='hs-conid'>Nothing</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>[]</span>
<a name="line-73"></a>
<a name="line-74"></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-75"></a> <span class='hs-keyglyph'>|</span> <span class='hs-varid'>touchesSegExtent</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-varid'>extent</span>
<a name="line-76"></a> <span class='hs-keyglyph'>-></span> <span class='hs-varid'>concat</span>
<a name="line-77"></a> <span class='hs-keyglyph'>[</span> <span class='hs-varid'>traceSegIntoCellularQuadTree</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-layout'>(</span><span class='hs-varid'>cutQuadOfExtent</span> <span class='hs-conid'>NW</span> <span class='hs-varid'>extent</span><span class='hs-layout'>)</span> <span class='hs-varid'>nw</span>
<a name="line-78"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>traceSegIntoCellularQuadTree</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-layout'>(</span><span class='hs-varid'>cutQuadOfExtent</span> <span class='hs-conid'>NE</span> <span class='hs-varid'>extent</span><span class='hs-layout'>)</span> <span class='hs-varid'>ne</span>
<a name="line-79"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>traceSegIntoCellularQuadTree</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-layout'>(</span><span class='hs-varid'>cutQuadOfExtent</span> <span class='hs-conid'>SW</span> <span class='hs-varid'>extent</span><span class='hs-layout'>)</span> <span class='hs-varid'>sw</span>
<a name="line-80"></a> <span class='hs-layout'>,</span> <span class='hs-varid'>traceSegIntoCellularQuadTree</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-layout'>(</span><span class='hs-varid'>cutQuadOfExtent</span> <span class='hs-conid'>SE</span> <span class='hs-varid'>extent</span><span class='hs-layout'>)</span> <span class='hs-varid'>se</span> <span class='hs-keyglyph'>]</span>
<a name="line-81"></a>
<a name="line-82"></a> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>-></span> <span class='hs-conid'>[]</span>
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