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<link rel="stylesheet" href="../coverage.css"/> <title> walkmap/edge.clj </title>
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<span class="covered" title="1 out of 1 forms covered">
001&nbsp;&nbsp;(ns&nbsp;walkmap.edge
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<span class="not-tracked" title="0 out of 0 forms covered">
002&nbsp;&nbsp;&nbsp;&nbsp;&quot;Essentially&nbsp;the&nbsp;specification&nbsp;for&nbsp;things&nbsp;we&nbsp;shall&nbsp;consider&nbsp;to&nbsp;be&nbsp;an&nbsp;edge.
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<span class="not-tracked" title="0 out of 0 forms covered">
003&nbsp;&nbsp;&nbsp;&nbsp;An&nbsp;edge&nbsp;is&nbsp;a&nbsp;line&nbsp;segment&nbsp;having&nbsp;just&nbsp;a&nbsp;start&nbsp;and&nbsp;an&nbsp;end,&nbsp;with&nbsp;no&nbsp;intervening
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<span class="not-tracked" title="0 out of 0 forms covered">
004&nbsp;&nbsp;&nbsp;&nbsp;nodes.&quot;
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<span class="not-tracked" title="0 out of 0 forms covered">
005&nbsp;&nbsp;&nbsp;&nbsp;(:require&nbsp;[clojure.math.numeric-tower&nbsp;:as&nbsp;m]
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<span class="not-tracked" title="0 out of 0 forms covered">
006&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[walkmap.utils&nbsp;:as&nbsp;u]
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<span class="not-tracked" title="0 out of 0 forms covered">
007&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[walkmap.vertex&nbsp;:refer&nbsp;[canonicalise&nbsp;ensure2d&nbsp;ensure3d&nbsp;vertex&nbsp;vertex=&nbsp;vertex?]]))
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<span class="blank" title="0 out of 0 forms covered">
008&nbsp;&nbsp;
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<span class="covered" title="1 out of 1 forms covered">
009&nbsp;&nbsp;(defn&nbsp;edge
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<span class="not-tracked" title="0 out of 0 forms covered">
010&nbsp;&nbsp;&nbsp;&nbsp;&quot;Return&nbsp;an&nbsp;edge&nbsp;between&nbsp;vertices&nbsp;`v1`&nbsp;and&nbsp;`v2`.&quot;
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<span class="not-tracked" title="0 out of 0 forms covered">
011&nbsp;&nbsp;&nbsp;&nbsp;[v1&nbsp;v2]
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<span class="covered" title="1 out of 1 forms covered">
012&nbsp;&nbsp;&nbsp;&nbsp;(if
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<span class="covered" title="10 out of 10 forms covered">
013&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(and&nbsp;(vertex?&nbsp;v1)&nbsp;(vertex?&nbsp;v2))
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<span class="covered" title="13 out of 13 forms covered">
014&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{:kind&nbsp;:edge&nbsp;:walkmap.id&#x2F;id&nbsp;(keyword&nbsp;(gensym&nbsp;&quot;edge&quot;))&nbsp;:start&nbsp;v1&nbsp;:end&nbsp;v2}
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<span class="covered" title="3 out of 3 forms covered">
015&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(throw&nbsp;(IllegalArgumentException.&nbsp;&quot;Must&nbsp;be&nbsp;vertices.&quot;))))
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<span class="blank" title="0 out of 0 forms covered">
016&nbsp;&nbsp;
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<span class="covered" title="1 out of 1 forms covered">
017&nbsp;&nbsp;(defn&nbsp;edge?
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<span class="not-tracked" title="0 out of 0 forms covered">
018&nbsp;&nbsp;&nbsp;&nbsp;&quot;True&nbsp;if&nbsp;`o`&nbsp;satisfies&nbsp;the&nbsp;conditions&nbsp;for&nbsp;a&nbsp;edge.&nbsp;An&nbsp;edge&nbsp;shall&nbsp;be&nbsp;a&nbsp;map
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
019&nbsp;&nbsp;&nbsp;&nbsp;having&nbsp;the&nbsp;keys&nbsp;`:start`&nbsp;and&nbsp;`:end`,&nbsp;such&nbsp;that&nbsp;the&nbsp;values&nbsp;of&nbsp;each&nbsp;of&nbsp;those
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<span class="not-tracked" title="0 out of 0 forms covered">
020&nbsp;&nbsp;&nbsp;&nbsp;keys&nbsp;shall&nbsp;be&nbsp;a&nbsp;vertex.&quot;
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<span class="not-tracked" title="0 out of 0 forms covered">
021&nbsp;&nbsp;&nbsp;&nbsp;[o]
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<span class="covered" title="9 out of 9 forms covered">
022&nbsp;&nbsp;&nbsp;&nbsp;(and
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<span class="covered" title="3 out of 3 forms covered">
023&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(map?&nbsp;o)
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<span class="covered" title="5 out of 5 forms covered">
024&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(vertex?&nbsp;(:start&nbsp;o))
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<span class="covered" title="4 out of 4 forms covered">
025&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(vertex?&nbsp;(:end&nbsp;o))))
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<span class="blank" title="0 out of 0 forms covered">
026&nbsp;&nbsp;
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<span class="covered" title="1 out of 1 forms covered">
027&nbsp;&nbsp;(defn&nbsp;length
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<span class="not-tracked" title="0 out of 0 forms covered">
028&nbsp;&nbsp;&nbsp;&nbsp;&quot;Return&nbsp;the&nbsp;length&nbsp;of&nbsp;the&nbsp;edge&nbsp;`e`.&quot;
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<span class="not-tracked" title="0 out of 0 forms covered">
029&nbsp;&nbsp;&nbsp;&nbsp;[e]
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<span class="covered" title="6 out of 6 forms covered">
030&nbsp;&nbsp;&nbsp;&nbsp;(let&nbsp;[start&nbsp;(ensure3d&nbsp;(:start&nbsp;e))
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<span class="covered" title="5 out of 5 forms covered">
031&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;end&nbsp;(ensure3d&nbsp;(:end&nbsp;e))]
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<span class="covered" title="2 out of 2 forms covered">
032&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(m&#x2F;sqrt
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<span class="covered" title="2 out of 2 forms covered">
033&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(reduce
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
034&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;+
</span><br/>
<span class="covered" title="3 out of 3 forms covered">
035&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(map
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<span class="covered" title="11 out of 11 forms covered">
036&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;#(m&#x2F;expt&nbsp;(-&nbsp;(%&nbsp;end)&nbsp;(%&nbsp;start))&nbsp;2)
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<span class="covered" title="4 out of 4 forms covered">
037&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[:x&nbsp;:y&nbsp;:z])))))
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<span class="blank" title="0 out of 0 forms covered">
038&nbsp;&nbsp;
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
039&nbsp;&nbsp;(defn&nbsp;centre
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<span class="not-tracked" title="0 out of 0 forms covered">
040&nbsp;&nbsp;&nbsp;&nbsp;&quot;Return&nbsp;the&nbsp;vertex&nbsp;that&nbsp;represents&nbsp;the&nbsp;centre&nbsp;of&nbsp;this&nbsp;`edge`.&quot;
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<span class="not-tracked" title="0 out of 0 forms covered">
041&nbsp;&nbsp;&nbsp;&nbsp;[edge]
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<span class="covered" title="6 out of 6 forms covered">
042&nbsp;&nbsp;&nbsp;&nbsp;(let&nbsp;[s&nbsp;(ensure3d&nbsp;(:start&nbsp;edge))
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<span class="covered" title="5 out of 5 forms covered">
043&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;e&nbsp;(ensure3d&nbsp;(:end&nbsp;edge))]
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<span class="covered" title="2 out of 2 forms covered">
044&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(vertex
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<span class="covered" title="16 out of 16 forms covered">
045&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(+&nbsp;(:x&nbsp;s)&nbsp;(&#x2F;&nbsp;(-&nbsp;(:x&nbsp;e)&nbsp;(:x&nbsp;s))&nbsp;2))
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<span class="covered" title="16 out of 16 forms covered">
046&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(+&nbsp;(:y&nbsp;s)&nbsp;(&#x2F;&nbsp;(-&nbsp;(:y&nbsp;e)&nbsp;(:y&nbsp;s))&nbsp;2))
</span><br/>
<span class="covered" title="16 out of 16 forms covered">
047&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(+&nbsp;(:z&nbsp;s)&nbsp;(&#x2F;&nbsp;(-&nbsp;(:z&nbsp;e)&nbsp;(:z&nbsp;s))&nbsp;2)))))
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<span class="blank" title="0 out of 0 forms covered">
048&nbsp;&nbsp;
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<span class="covered" title="1 out of 1 forms covered">
049&nbsp;&nbsp;(defn&nbsp;unit-vector
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<span class="not-tracked" title="0 out of 0 forms covered">
050&nbsp;&nbsp;&nbsp;&nbsp;&quot;Return&nbsp;an&nbsp;vertex&nbsp;parallel&nbsp;to&nbsp;`e`&nbsp;starting&nbsp;from&nbsp;the&nbsp;coordinate&nbsp;origin.&nbsp;Two
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
051&nbsp;&nbsp;&nbsp;&nbsp;edges&nbsp;which&nbsp;are&nbsp;parallel&nbsp;will&nbsp;have&nbsp;the&nbsp;same&nbsp;unit&nbsp;vector.&quot;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
052&nbsp;&nbsp;&nbsp;&nbsp;[e]
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<span class="covered" title="14 out of 14 forms covered">
053&nbsp;&nbsp;&nbsp;&nbsp;(let&nbsp;[e&#x27;&nbsp;{:start&nbsp;(ensure3d&nbsp;(:start&nbsp;e))&nbsp;:end&nbsp;(ensure3d&nbsp;(:end&nbsp;e))}
</span><br/>
<span class="covered" title="3 out of 3 forms covered">
054&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;l&nbsp;(length&nbsp;e&#x27;)]
</span><br/>
<span class="covered" title="2 out of 2 forms covered">
055&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(canonicalise
</span><br/>
<span class="covered" title="2 out of 2 forms covered">
056&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(reduce
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
057&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;merge
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
058&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{}
</span><br/>
<span class="covered" title="2 out of 2 forms covered">
059&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(map
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
060&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(fn&nbsp;[k]
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<span class="covered" title="17 out of 17 forms covered">
061&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{k&nbsp;(&#x2F;&nbsp;(-&nbsp;(k&nbsp;(:end&nbsp;e&#x27;))&nbsp;(k&nbsp;(:start&nbsp;e&#x27;)))&nbsp;l)})
</span><br/>
<span class="covered" title="4 out of 4 forms covered">
062&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[:x&nbsp;:y&nbsp;:z])))))
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<span class="blank" title="0 out of 0 forms covered">
063&nbsp;&nbsp;
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
064&nbsp;&nbsp;(defn&nbsp;parallel?
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<span class="not-tracked" title="0 out of 0 forms covered">
065&nbsp;&nbsp;&nbsp;&nbsp;&quot;True&nbsp;if&nbsp;all&nbsp;`edges`&nbsp;passed&nbsp;are&nbsp;parallel&nbsp;with&nbsp;one&nbsp;another.&quot;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
066&nbsp;&nbsp;&nbsp;&nbsp;[&amp;&nbsp;edges]
</span><br/>
<span class="covered" title="5 out of 5 forms covered">
067&nbsp;&nbsp;&nbsp;&nbsp;(let&nbsp;[uvs&nbsp;(map&nbsp;unit-vector&nbsp;edges)]
</span><br/>
<span class="covered" title="3 out of 3 forms covered">
068&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(every?
</span><br/>
<span class="covered" title="6 out of 6 forms covered">
069&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;#(vertex=&nbsp;%&nbsp;(first&nbsp;uvs))
</span><br/>
<span class="covered" title="3 out of 3 forms covered">
070&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(rest&nbsp;uvs))))
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
071&nbsp;&nbsp;
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
072&nbsp;&nbsp;(defn&nbsp;collinear?
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
073&nbsp;&nbsp;&nbsp;&nbsp;&quot;True&nbsp;if&nbsp;edges&nbsp;`e1`&nbsp;and&nbsp;`e2`&nbsp;are&nbsp;collinear&nbsp;with&nbsp;one&nbsp;another.&quot;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
074&nbsp;&nbsp;&nbsp;&nbsp;[e1&nbsp;e2]
</span><br/>
<span class="covered" title="2 out of 2 forms covered">
075&nbsp;&nbsp;&nbsp;&nbsp;(parallel?
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
076&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;e1
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
077&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;e2
</span><br/>
<span class="covered" title="9 out of 9 forms covered">
078&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(if&nbsp;(vertex=&nbsp;(:start&nbsp;e1)&nbsp;(:start&nbsp;e2))
</span><br/>
<span class="covered" title="9 out of 9 forms covered">
079&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{:start&nbsp;(:start&nbsp;e1)&nbsp;:end&nbsp;(:end&nbsp;e2)}
</span><br/>
<span class="covered" title="9 out of 9 forms covered">
080&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{:start&nbsp;(:start&nbsp;e1)&nbsp;:end&nbsp;(:start&nbsp;e2)})))
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
081&nbsp;&nbsp;
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
082&nbsp;&nbsp;(defn&nbsp;collinear2d?
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
083&nbsp;&nbsp;&nbsp;&nbsp;&quot;True&nbsp;if&nbsp;the&nbsp;projections&nbsp;of&nbsp;edges&nbsp;`e1`,&nbsp;`e2`&nbsp;onto&nbsp;the&nbsp;x,&nbsp;y&nbsp;plane&nbsp;are
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
084&nbsp;&nbsp;&nbsp;&nbsp;collinear.&quot;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
085&nbsp;&nbsp;&nbsp;&nbsp;[e1&nbsp;e2]
</span><br/>
<span class="covered" title="15 out of 15 forms covered">
086&nbsp;&nbsp;&nbsp;&nbsp;(collinear?&nbsp;{:start&nbsp;(ensure2d&nbsp;(:start&nbsp;e1))&nbsp;:end&nbsp;(ensure2d&nbsp;(:end&nbsp;e1))}
</span><br/>
<span class="covered" title="13 out of 13 forms covered">
087&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{:start&nbsp;(ensure2d&nbsp;(:start&nbsp;e2))&nbsp;:end&nbsp;(ensure2d&nbsp;(:end&nbsp;e2))}))
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
088&nbsp;&nbsp;
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
089&nbsp;&nbsp;(defn&nbsp;minimaxd
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
090&nbsp;&nbsp;&nbsp;&nbsp;&quot;Apply&nbsp;function&nbsp;`f`&nbsp;to&nbsp;`coord`&nbsp;of&nbsp;the&nbsp;vertices&nbsp;at&nbsp;start&nbsp;and&nbsp;end&nbsp;of&nbsp;`edge`
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
091&nbsp;&nbsp;&nbsp;&nbsp;and&nbsp;return&nbsp;the&nbsp;result.&nbsp;Intended&nbsp;use&nbsp;case&nbsp;is&nbsp;`f`&nbsp;=&nbsp;`min`&nbsp;or&nbsp;`max`,&nbsp;`coord`
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
092&nbsp;&nbsp;&nbsp;&nbsp;is&nbsp;`:x`,&nbsp;`:y`&nbsp;or&nbsp;`:z`.&nbsp;No&nbsp;checks&nbsp;are&nbsp;made&nbsp;for&nbsp;sane&nbsp;arguments.&quot;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
093&nbsp;&nbsp;&nbsp;&nbsp;[edge&nbsp;coord&nbsp;f]
</span><br/>
<span class="covered" title="15 out of 15 forms covered">
094&nbsp;&nbsp;&nbsp;&nbsp;(apply&nbsp;f&nbsp;(list&nbsp;(coord&nbsp;(:start&nbsp;edge))&nbsp;(coord&nbsp;(:end&nbsp;edge)))))
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
095&nbsp;&nbsp;
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
096&nbsp;&nbsp;(defn&nbsp;on?
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
097&nbsp;&nbsp;&nbsp;&nbsp;&quot;True&nbsp;if&nbsp;the&nbsp;vertex&nbsp;`v`&nbsp;is&nbsp;on&nbsp;the&nbsp;edge&nbsp;`e`.&quot;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
098&nbsp;&nbsp;&nbsp;&nbsp;[e&nbsp;v]
</span><br/>
<span class="covered" title="6 out of 6 forms covered">
099&nbsp;&nbsp;&nbsp;&nbsp;(let&nbsp;[p&nbsp;(ensure3d&nbsp;(:start&nbsp;e))
</span><br/>
<span class="covered" title="3 out of 3 forms covered">
100&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;q&nbsp;(ensure3d&nbsp;v)
</span><br/>
<span class="covered" title="5 out of 5 forms covered">
101&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;r&nbsp;(ensure3d&nbsp;(:end&nbsp;e))]
</span><br/>
<span class="partial" title="20 out of 25 forms covered">
102&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(and
</span><br/>
<span class="covered" title="10 out of 10 forms covered">
103&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(collinear?&nbsp;(edge&nbsp;p&nbsp;q)&nbsp;(edge&nbsp;q&nbsp;r))
</span><br/>
<span class="covered" title="13 out of 13 forms covered">
104&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&lt;=&nbsp;(:x&nbsp;q)&nbsp;(max&nbsp;(:x&nbsp;p)&nbsp;(:x&nbsp;r)))
</span><br/>
<span class="covered" title="13 out of 13 forms covered">
105&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&gt;=&nbsp;(:x&nbsp;q)&nbsp;(min&nbsp;(:x&nbsp;p)&nbsp;(:x&nbsp;r)))
</span><br/>
<span class="covered" title="13 out of 13 forms covered">
106&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&lt;=&nbsp;(:y&nbsp;q)&nbsp;(max&nbsp;(:y&nbsp;p)&nbsp;(:y&nbsp;r)))
</span><br/>
<span class="covered" title="13 out of 13 forms covered">
107&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&gt;=&nbsp;(:y&nbsp;q)&nbsp;(min&nbsp;(:y&nbsp;p)&nbsp;(:y&nbsp;r)))
</span><br/>
<span class="covered" title="13 out of 13 forms covered">
108&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&lt;=&nbsp;(:z&nbsp;q)&nbsp;(max&nbsp;(:z&nbsp;p)&nbsp;(:z&nbsp;r)))
</span><br/>
<span class="covered" title="12 out of 12 forms covered">
109&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&gt;=&nbsp;(:z&nbsp;q)&nbsp;(min&nbsp;(:z&nbsp;p)&nbsp;(:z&nbsp;r))))))
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
110&nbsp;&nbsp;
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
111&nbsp;&nbsp;(defn&nbsp;on2d?
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
112&nbsp;&nbsp;&nbsp;&nbsp;&quot;True&nbsp;if&nbsp;vertex&nbsp;`v`&nbsp;is&nbsp;on&nbsp;edge&nbsp;`e`&nbsp;when&nbsp;projected&nbsp;onto&nbsp;the&nbsp;x,&nbsp;y&nbsp;plane.&quot;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
113&nbsp;&nbsp;&nbsp;&nbsp;[e&nbsp;v]
</span><br/>
<span class="covered" title="15 out of 15 forms covered">
114&nbsp;&nbsp;&nbsp;&nbsp;(on?&nbsp;(edge&nbsp;(ensure2d&nbsp;(:start&nbsp;e))&nbsp;(ensure2d&nbsp;(:end&nbsp;e)))&nbsp;v))
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
115&nbsp;&nbsp;
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
116&nbsp;&nbsp;(defn&nbsp;overlaps2d?
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
117&nbsp;&nbsp;&nbsp;&nbsp;&quot;True&nbsp;if&nbsp;the&nbsp;recangle&nbsp;in&nbsp;the&nbsp;x,y&nbsp;plane&nbsp;bisected&nbsp;by&nbsp;edge&nbsp;`e1`&nbsp;overlaps&nbsp;that
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
118&nbsp;&nbsp;&nbsp;&nbsp;bisected&nbsp;by&nbsp;edge&nbsp;`e2`.&nbsp;It&nbsp;is&nbsp;an&nbsp;error&nbsp;if&nbsp;either&nbsp;`e1`&nbsp;or&nbsp;`e2`&nbsp;is&nbsp;not&nbsp;an&nbsp;edge.&quot;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
119&nbsp;&nbsp;&nbsp;&nbsp;[e1&nbsp;e2]
</span><br/>
<span class="partial" title="11 out of 12 forms covered">
120&nbsp;&nbsp;&nbsp;&nbsp;(when&nbsp;(and&nbsp;(edge?&nbsp;e1)&nbsp;(edge?&nbsp;e2))
</span><br/>
<span class="partial" title="11 out of 13 forms covered">
121&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(and
</span><br/>
<span class="covered" title="12 out of 12 forms covered">
122&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&gt;&nbsp;(minimaxd&nbsp;e1&nbsp;:x&nbsp;max)&nbsp;(minimaxd&nbsp;e2&nbsp;:x&nbsp;min))
</span><br/>
<span class="covered" title="12 out of 12 forms covered">
123&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&lt;&nbsp;(minimaxd&nbsp;e1&nbsp;:x&nbsp;min)&nbsp;(minimaxd&nbsp;e2&nbsp;:x&nbsp;max))
</span><br/>
<span class="covered" title="12 out of 12 forms covered">
124&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&gt;&nbsp;(minimaxd&nbsp;e1&nbsp;:y&nbsp;max)&nbsp;(minimaxd&nbsp;e2&nbsp;:y&nbsp;min))
</span><br/>
<span class="covered" title="11 out of 11 forms covered">
125&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(&lt;&nbsp;(minimaxd&nbsp;e1&nbsp;:y&nbsp;min)&nbsp;(minimaxd&nbsp;e2&nbsp;:y&nbsp;max)))))
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
126&nbsp;&nbsp;
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
127&nbsp;&nbsp;(defn&nbsp;intersection2d
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
128&nbsp;&nbsp;&nbsp;&nbsp;&quot;The&nbsp;probability&nbsp;of&nbsp;two&nbsp;lines&nbsp;intersecting&nbsp;in&nbsp;3d&nbsp;space&nbsp;is&nbsp;low,&nbsp;and&nbsp;actually
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
129&nbsp;&nbsp;&nbsp;&nbsp;that&nbsp;is&nbsp;mostly&nbsp;not&nbsp;something&nbsp;we&#x27;re&nbsp;interested&nbsp;in.&nbsp;We&#x27;re&nbsp;interested&nbsp;in
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
130&nbsp;&nbsp;&nbsp;&nbsp;intersection&nbsp;in&nbsp;the&nbsp;`x,y`&nbsp;plane.&nbsp;This&nbsp;function&nbsp;returns&nbsp;a&nbsp;vertex&nbsp;representing
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
131&nbsp;&nbsp;&nbsp;&nbsp;a&nbsp;point&nbsp;vertically&nbsp;over&nbsp;the&nbsp;intersection&nbsp;of&nbsp;edges&nbsp;`e1`,&nbsp;`e2`&nbsp;in&nbsp;the&nbsp;`x,y`
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
132&nbsp;&nbsp;&nbsp;&nbsp;plane,&nbsp;whose&nbsp;`z`&nbsp;coordinate&nbsp;is
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
133&nbsp;&nbsp;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
134&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;0&nbsp;if&nbsp;both&nbsp;edges&nbsp;are&nbsp;2d&nbsp;(i.e.&nbsp;have&nbsp;missing&nbsp;or&nbsp;zero&nbsp;`z`&nbsp;coordinates);
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
135&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;if&nbsp;one&nbsp;edge&nbsp;is&nbsp;2d,&nbsp;then&nbsp;the&nbsp;point&nbsp;on&nbsp;the&nbsp;other&nbsp;edge&nbsp;over&nbsp;the&nbsp;intersection;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
136&nbsp;&nbsp;&nbsp;&nbsp;*&nbsp;otherwise,&nbsp;the&nbsp;average&nbsp;of&nbsp;the&nbsp;z&nbsp;coordinates&nbsp;of&nbsp;the&nbsp;points&nbsp;on&nbsp;the&nbsp;two
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
137&nbsp;&nbsp;&nbsp;&nbsp;edges&nbsp;over&nbsp;the&nbsp;intersection.
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
138&nbsp;&nbsp;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
139&nbsp;&nbsp;&nbsp;&nbsp;If&nbsp;no&nbsp;such&nbsp;intersection&nbsp;exists,&nbsp;`nil`&nbsp;is&nbsp;returned.
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
140&nbsp;&nbsp;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
141&nbsp;&nbsp;&nbsp;&nbsp;It&nbsp;is&nbsp;an&nbsp;error,&nbsp;and&nbsp;an&nbsp;exception&nbsp;will&nbsp;be&nbsp;thrown,&nbsp;if&nbsp;either&nbsp;`e1`&nbsp;or&nbsp;`e2`&nbsp;is
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
142&nbsp;&nbsp;&nbsp;&nbsp;not&nbsp;an&nbsp;edge.&quot;
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
143&nbsp;&nbsp;&nbsp;&nbsp;[e1&nbsp;e2]
</span><br/>
<span class="covered" title="11 out of 11 forms covered">
144&nbsp;&nbsp;&nbsp;&nbsp;(if&nbsp;(and&nbsp;(edge?&nbsp;e1)&nbsp;(edge?&nbsp;e2))
</span><br/>
<span class="covered" title="2 out of 2 forms covered">
145&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(when
</span><br/>
<span class="covered" title="4 out of 4 forms covered">
146&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(overlaps2d?&nbsp;e1&nbsp;e2)&nbsp;;;&nbsp;relatively&nbsp;cheap&nbsp;check
</span><br/>
<span class="covered" title="1 out of 1 forms covered">
147&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(if
</span><br/>
<span class="covered" title="4 out of 4 forms covered">
148&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(collinear2d?&nbsp;e1&nbsp;e2)
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
149&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;;&nbsp;any&nbsp;point&nbsp;within&nbsp;the&nbsp;overlap&nbsp;will&nbsp;do,&nbsp;but&nbsp;we&#x27;ll&nbsp;pick&nbsp;the&nbsp;end&nbsp;of&nbsp;e1
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
150&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;;&nbsp;which&nbsp;is&nbsp;on&nbsp;e2
</span><br/>
<span class="partial" title="10 out of 13 forms covered">
151&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(if&nbsp;(on2d?&nbsp;e2&nbsp;(:start&nbsp;e1))&nbsp;(:start&nbsp;e1)&nbsp;(:end&nbsp;e1))
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
152&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;;&nbsp;blatantly&nbsp;stolen&nbsp;from
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
153&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;;;&nbsp;https:&#x2F;&#x2F;gist.github.com&#x2F;cassiel&#x2F;3e725b49670356a9b936
</span><br/>
<span class="covered" title="6 out of 6 forms covered">
154&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(let&nbsp;[x1&nbsp;(:x&nbsp;(:start&nbsp;e1))
</span><br/>
<span class="covered" title="5 out of 5 forms covered">
155&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x2&nbsp;(:x&nbsp;(:end&nbsp;e1))
</span><br/>
<span class="covered" title="5 out of 5 forms covered">
156&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x3&nbsp;(:x&nbsp;(:start&nbsp;e2))
</span><br/>
<span class="covered" title="5 out of 5 forms covered">
157&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x4&nbsp;(:x&nbsp;(:end&nbsp;e2))
</span><br/>
<span class="covered" title="5 out of 5 forms covered">
158&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y1&nbsp;(:y&nbsp;(:start&nbsp;e1))
</span><br/>
<span class="covered" title="5 out of 5 forms covered">
159&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y2&nbsp;(:y&nbsp;(:end&nbsp;e1))
</span><br/>
<span class="covered" title="5 out of 5 forms covered">
160&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y3&nbsp;(:y&nbsp;(:start&nbsp;e2))
</span><br/>
<span class="covered" title="5 out of 5 forms covered">
161&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;y4&nbsp;(:y&nbsp;(:end&nbsp;e2))
</span><br/>
<span class="covered" title="12 out of 12 forms covered">
162&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;denom&nbsp;(-&nbsp;(*&nbsp;(-&nbsp;x1&nbsp;x2)&nbsp;(-&nbsp;y3&nbsp;y4))
</span><br/>
<span class="covered" title="10 out of 10 forms covered">
163&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(*&nbsp;(-&nbsp;y1&nbsp;y2)&nbsp;(-&nbsp;x3&nbsp;x4)))
</span><br/>
<span class="covered" title="10 out of 10 forms covered">
164&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x1y2-y1x2&nbsp;(-&nbsp;(*&nbsp;x1&nbsp;y2)&nbsp;(*&nbsp;y1&nbsp;x2))
</span><br/>
<span class="covered" title="10 out of 10 forms covered">
165&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;x3y4-y3x4&nbsp;(-&nbsp;(*&nbsp;x3&nbsp;y4)&nbsp;(*&nbsp;y3&nbsp;x4))
</span><br/>
<span class="covered" title="9 out of 9 forms covered">
166&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;px-num&nbsp;(-&nbsp;(*&nbsp;x1y2-y1x2&nbsp;(-&nbsp;x3&nbsp;x4))
</span><br/>
<span class="covered" title="7 out of 7 forms covered">
167&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(*&nbsp;(-&nbsp;x1&nbsp;x2)&nbsp;x3y4-y3x4))
</span><br/>
<span class="covered" title="9 out of 9 forms covered">
168&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;py-num&nbsp;(-&nbsp;(*&nbsp;x1y2-y1x2&nbsp;(-&nbsp;y3&nbsp;y4))
</span><br/>
<span class="covered" title="7 out of 7 forms covered">
169&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(*&nbsp;(-&nbsp;y1&nbsp;y2)&nbsp;x3y4-y3x4))
</span><br/>
<span class="covered" title="6 out of 6 forms covered">
170&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;result&nbsp;(when-not&nbsp;(zero?&nbsp;denom)
</span><br/>
<span class="covered" title="10 out of 10 forms covered">
171&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(vertex&nbsp;(&#x2F;&nbsp;px-num&nbsp;denom)&nbsp;(&#x2F;&nbsp;py-num&nbsp;denom)))]
</span><br/>
<span class="partial" title="19 out of 20 forms covered">
172&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(when&nbsp;(and&nbsp;result&nbsp;(on2d?&nbsp;e1&nbsp;result)&nbsp;(on2d?&nbsp;e2&nbsp;result))&nbsp;result))))
</span><br/>
<span class="covered" title="2 out of 2 forms covered">
173&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(throw&nbsp;(IllegalArgumentException.
</span><br/>
<span class="covered" title="3 out of 3 forms covered">
174&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(str
</span><br/>
<span class="not-tracked" title="0 out of 0 forms covered">
175&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&quot;Both&nbsp;`e1`&nbsp;and&nbsp;`e2`&nbsp;must&nbsp;be&nbsp;edges.&quot;
</span><br/>
<span class="covered" title="16 out of 16 forms covered">
176&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(map&nbsp;#(or&nbsp;(:kind&nbsp;%)&nbsp;(type&nbsp;%))&nbsp;[e1&nbsp;e2]))))))
</span><br/>
<span class="blank" title="0 out of 0 forms covered">
177&nbsp;&nbsp;
</span><br/>
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