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<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html>
<head>
<!-- Generated by HsColour, http://code.haskell.org/~malcolm/hscolour/ -->
<title>Graphics/Rendering/Chart/Geometry.hs</title>
<link type='text/css' rel='stylesheet' href='hscolour.css' />
</head>
<body>
<pre><a name="line-1"></a><span class='hs-comment'>-----------------------------------------------------------------------------</span>
<a name="line-2"></a><span class='hs-comment'>-- |</span>
<a name="line-3"></a><span class='hs-comment'>-- Module      :  Graphics.Rendering.Chart.Geometry</span>
<a name="line-4"></a><span class='hs-comment'>-- Copyright   :  (c) Tim Docker 2006, 2014</span>
<a name="line-5"></a><span class='hs-comment'>-- License     :  BSD-style (see chart/COPYRIGHT)</span>
<a name="line-6"></a><span class='hs-comment'>--</span>
<a name="line-7"></a><span class='hs-keyword'>module</span> <span class='hs-conid'>Graphics</span><span class='hs-varop'>.</span><span class='hs-conid'>Rendering</span><span class='hs-varop'>.</span><span class='hs-conid'>Chart</span><span class='hs-varop'>.</span><span class='hs-conid'>Geometry</span>
<a name="line-8"></a>  <span class='hs-layout'>(</span> <span class='hs-comment'>-- * Points and Vectors</span>
<a name="line-9"></a>    <span class='hs-conid'>Rect</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-10"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Point</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-11"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Vector</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-12"></a>
<a name="line-13"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>RectSize</span>
<a name="line-14"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Range</span>
<a name="line-15"></a>
<a name="line-16"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>pointToVec</span>
<a name="line-17"></a>
<a name="line-18"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>mkrect</span>
<a name="line-19"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>rectPath</span>
<a name="line-20"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>pvadd</span>
<a name="line-21"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>pvsub</span>
<a name="line-22"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>psub</span>
<a name="line-23"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>vangle</span>
<a name="line-24"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>vlen</span>
<a name="line-25"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>vscale</span>
<a name="line-26"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>within</span>
<a name="line-27"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>intersectRect</span>
<a name="line-28"></a>
<a name="line-29"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>RectEdge</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-30"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Limit</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-31"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>PointMapFn</span>
<a name="line-32"></a>
<a name="line-33"></a>  <span class='hs-comment'>-- * Paths</span>
<a name="line-34"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Path</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-35"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>lineTo</span><span class='hs-layout'>,</span> <span class='hs-varid'>moveTo</span>
<a name="line-36"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>lineTo'</span><span class='hs-layout'>,</span> <span class='hs-varid'>moveTo'</span>
<a name="line-37"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>arc</span><span class='hs-layout'>,</span> <span class='hs-varid'>arc'</span>
<a name="line-38"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>arcNeg</span><span class='hs-layout'>,</span> <span class='hs-varid'>arcNeg'</span>
<a name="line-39"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>close</span>
<a name="line-40"></a>
<a name="line-41"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>foldPath</span>
<a name="line-42"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>makeLinesExplicit</span>
<a name="line-43"></a>
<a name="line-44"></a>  <span class='hs-comment'>-- * Matrices</span>
<a name="line-45"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>transformP</span><span class='hs-layout'>,</span> <span class='hs-varid'>scaleP</span><span class='hs-layout'>,</span> <span class='hs-varid'>rotateP</span><span class='hs-layout'>,</span> <span class='hs-varid'>translateP</span>
<a name="line-46"></a>  <span class='hs-layout'>,</span> <span class='hs-conid'>Matrix</span><span class='hs-layout'>(</span><span class='hs-keyglyph'>..</span><span class='hs-layout'>)</span>
<a name="line-47"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>identity</span>
<a name="line-48"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>rotate</span><span class='hs-layout'>,</span> <span class='hs-varid'>scale</span><span class='hs-layout'>,</span> <span class='hs-varid'>translate</span>
<a name="line-49"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>scalarMultiply</span>
<a name="line-50"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>adjoint</span>
<a name="line-51"></a>  <span class='hs-layout'>,</span> <span class='hs-varid'>invert</span>
<a name="line-52"></a>  <span class='hs-layout'>)</span> <span class='hs-keyword'>where</span>
<a name="line-53"></a>
<a name="line-54"></a><span class='hs-keyword'>import</span> <span class='hs-keyword'>qualified</span> <span class='hs-conid'>Prelude</span>
<a name="line-55"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Prelude</span> <span class='hs-varid'>hiding</span> <span class='hs-layout'>(</span><span class='hs-layout'>(</span><span class='hs-varop'>^</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-56"></a><span class='hs-keyword'>import</span> <span class='hs-conid'>Data</span><span class='hs-varop'>.</span><span class='hs-conid'>Monoid</span>
<a name="line-57"></a>
<a name="line-58"></a><a name="%5e"></a><span class='hs-comment'>-- The homomorphic version to avoid casts inside the code.</span>
<a name="line-59"></a><span class='hs-layout'>(</span><span class='hs-varop'>^</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Num</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=&gt;</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Integer</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>a</span>
<a name="line-60"></a><span class='hs-layout'>(</span><span class='hs-varop'>^</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Prelude</span><span class='hs-varop'>.^</span><span class='hs-layout'>)</span>
<a name="line-61"></a>
<a name="line-62"></a><a name="Point"></a><span class='hs-comment'>-- | A point in two dimensions.</span>
<a name="line-63"></a><a name="Point"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Point</span> <span class='hs-layout'>{</span>
<a name="line-64"></a>    <span class='hs-varid'>p_x</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span><span class='hs-layout'>,</span>
<a name="line-65"></a>    <span class='hs-varid'>p_y</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span>
<a name="line-66"></a><span class='hs-layout'>}</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Show</span>
<a name="line-67"></a>
<a name="line-68"></a><a name="Vector"></a><span class='hs-comment'>-- | A vector in two dimensions.</span>
<a name="line-69"></a><a name="Vector"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Vector</span> <span class='hs-layout'>{</span>
<a name="line-70"></a>    <span class='hs-varid'>v_x</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span><span class='hs-layout'>,</span>
<a name="line-71"></a>    <span class='hs-varid'>v_y</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span>
<a name="line-72"></a><span class='hs-layout'>}</span> <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Show</span>
<a name="line-73"></a>
<a name="line-74"></a><a name="pointToVec"></a><span class='hs-comment'>-- | Convert a 'Point' to a 'Vector'.</span>
<a name="line-75"></a><span class='hs-definition'>pointToVec</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Vector</span>
<a name="line-76"></a><span class='hs-definition'>pointToVec</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Vector</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span>
<a name="line-77"></a>
<a name="line-78"></a><a name="vangle"></a><span class='hs-comment'>-- | Angle of a vector (counterclockwise from positive x-axis)</span>
<a name="line-79"></a><span class='hs-definition'>vangle</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span>
<a name="line-80"></a><span class='hs-definition'>vangle</span> <span class='hs-layout'>(</span><span class='hs-conid'>Vector</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span>
<a name="line-81"></a>    <span class='hs-keyglyph'>|</span> <span class='hs-varid'>x</span> <span class='hs-varop'>&gt;</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>atan</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-varop'>/</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span>
<a name="line-82"></a>    <span class='hs-keyglyph'>|</span> <span class='hs-varid'>x</span> <span class='hs-varop'>&lt;</span> <span class='hs-num'>0</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>atan</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-varop'>/</span><span class='hs-varid'>x</span><span class='hs-layout'>)</span> <span class='hs-varop'>+</span> <span class='hs-varid'>pi</span>
<a name="line-83"></a>    <span class='hs-keyglyph'>|</span> <span class='hs-varid'>otherwise</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>y</span> <span class='hs-varop'>&gt;</span> <span class='hs-num'>0</span> <span class='hs-keyword'>then</span> <span class='hs-varid'>pi</span><span class='hs-varop'>/</span><span class='hs-num'>2</span> <span class='hs-keyword'>else</span> <span class='hs-comment'>-</span><span class='hs-varid'>pi</span><span class='hs-varop'>/</span><span class='hs-num'>2</span>
<a name="line-84"></a>
<a name="line-85"></a><a name="vlen"></a><span class='hs-comment'>-- | Length/magnitude of a vector</span>
<a name="line-86"></a><span class='hs-definition'>vlen</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span>
<a name="line-87"></a><span class='hs-definition'>vlen</span> <span class='hs-layout'>(</span><span class='hs-conid'>Vector</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sqrt</span> <span class='hs-varop'>$</span> <span class='hs-varid'>x</span><span class='hs-varop'>^</span><span class='hs-num'>2</span> <span class='hs-varop'>+</span> <span class='hs-varid'>y</span><span class='hs-varop'>^</span><span class='hs-num'>2</span>
<a name="line-88"></a>
<a name="line-89"></a><a name="vscale"></a><span class='hs-comment'>-- | Scale a vector by a constant.</span>
<a name="line-90"></a><span class='hs-definition'>vscale</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Vector</span>
<a name="line-91"></a><span class='hs-definition'>vscale</span> <span class='hs-varid'>c</span> <span class='hs-layout'>(</span><span class='hs-conid'>Vector</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Vector</span> <span class='hs-layout'>(</span><span class='hs-varid'>x</span><span class='hs-varop'>*</span><span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y</span><span class='hs-varop'>*</span><span class='hs-varid'>c</span><span class='hs-layout'>)</span>
<a name="line-92"></a>
<a name="line-93"></a><a name="pvadd"></a><span class='hs-comment'>-- | Add a point and a vector.</span>
<a name="line-94"></a><span class='hs-definition'>pvadd</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span>
<a name="line-95"></a><span class='hs-definition'>pvadd</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Vector</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Point</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-varop'>+</span><span class='hs-varid'>x2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y1</span><span class='hs-varop'>+</span><span class='hs-varid'>y2</span><span class='hs-layout'>)</span>
<a name="line-96"></a>
<a name="line-97"></a><a name="pvsub"></a><span class='hs-comment'>-- | Subtract a vector from a point.</span>
<a name="line-98"></a><span class='hs-definition'>pvsub</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span>
<a name="line-99"></a><span class='hs-definition'>pvsub</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Vector</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Point</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-comment'>-</span><span class='hs-varid'>x2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y1</span><span class='hs-comment'>-</span><span class='hs-varid'>y2</span><span class='hs-layout'>)</span>
<a name="line-100"></a>
<a name="line-101"></a><a name="psub"></a><span class='hs-comment'>-- | Subtract two points.</span>
<a name="line-102"></a><span class='hs-definition'>psub</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Vector</span>
<a name="line-103"></a><span class='hs-definition'>psub</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Vector</span> <span class='hs-layout'>(</span><span class='hs-varid'>x1</span><span class='hs-comment'>-</span><span class='hs-varid'>x2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>y1</span><span class='hs-comment'>-</span><span class='hs-varid'>y2</span><span class='hs-layout'>)</span>
<a name="line-104"></a>
<a name="line-105"></a><a name="Limit"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Limit</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LMin</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>LValue</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>LMax</span>
<a name="line-106"></a>   <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Show</span>
<a name="line-107"></a>
<a name="line-108"></a><a name="PointMapFn"></a><span class='hs-comment'>-- | A function mapping between points.</span>
<a name="line-109"></a><a name="PointMapFn"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>PointMapFn</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Limit</span> <span class='hs-varid'>x</span><span class='hs-layout'>,</span> <span class='hs-conid'>Limit</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span>
<a name="line-110"></a>
<a name="line-111"></a><a name="Rect"></a><span class='hs-comment'>-- | A rectangle is defined by two points.</span>
<a name="line-112"></a><a name="Rect"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Rect</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Rect</span> <span class='hs-conid'>Point</span> <span class='hs-conid'>Point</span>
<a name="line-113"></a>   <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Show</span>
<a name="line-114"></a>
<a name="line-115"></a><a name="RectEdge"></a><span class='hs-comment'>-- | Edge of a rectangle.</span>
<a name="line-116"></a><a name="RectEdge"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>RectEdge</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>E_Top</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>E_Bottom</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>E_Left</span> <span class='hs-keyglyph'>|</span> <span class='hs-conid'>E_Right</span>
<a name="line-117"></a>
<a name="line-118"></a><a name="mkrect"></a><span class='hs-comment'>-- | Create a rectangle based upon the coordinates of 4 points.</span>
<a name="line-119"></a><span class='hs-definition'>mkrect</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Rect</span>
<a name="line-120"></a><span class='hs-definition'>mkrect</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x1</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x3</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-keyword'>_</span> <span class='hs-varid'>y4</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-121"></a>    <span class='hs-conid'>Rect</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x3</span> <span class='hs-varid'>y4</span><span class='hs-layout'>)</span>
<a name="line-122"></a>
<a name="line-123"></a><a name="within"></a><span class='hs-comment'>-- | Test if a point is within a rectangle.</span>
<a name="line-124"></a><span class='hs-definition'>within</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Rect</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Bool</span>
<a name="line-125"></a><span class='hs-definition'>within</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rect</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-126"></a>    <span class='hs-varid'>x</span> <span class='hs-varop'>&gt;=</span> <span class='hs-varid'>x1</span> <span class='hs-varop'>&amp;&amp;</span> <span class='hs-varid'>x</span> <span class='hs-varop'>&lt;=</span> <span class='hs-varid'>x2</span> <span class='hs-varop'>&amp;&amp;</span> <span class='hs-varid'>y</span> <span class='hs-varop'>&gt;=</span> <span class='hs-varid'>y1</span> <span class='hs-varop'>&amp;&amp;</span> <span class='hs-varid'>y</span> <span class='hs-varop'>&lt;=</span> <span class='hs-varid'>y2</span>
<a name="line-127"></a>
<a name="line-128"></a><a name="intersectRect"></a><span class='hs-comment'>-- | Intersects the rectangles. If they intersect the</span>
<a name="line-129"></a><span class='hs-comment'>--   intersection rectangle is returned.</span>
<a name="line-130"></a><span class='hs-comment'>--   'LMin' is the empty rectangle / intersection and</span>
<a name="line-131"></a><span class='hs-comment'>--   'LMax' is the infinite plane.</span>
<a name="line-132"></a><span class='hs-definition'>intersectRect</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Limit</span> <span class='hs-conid'>Rect</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Limit</span> <span class='hs-conid'>Rect</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Limit</span> <span class='hs-conid'>Rect</span>
<a name="line-133"></a><span class='hs-definition'>intersectRect</span> <span class='hs-conid'>LMax</span> <span class='hs-varid'>r</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>r</span>
<a name="line-134"></a><span class='hs-definition'>intersectRect</span> <span class='hs-varid'>r</span> <span class='hs-conid'>LMax</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>r</span>
<a name="line-135"></a><span class='hs-definition'>intersectRect</span> <span class='hs-conid'>LMin</span> <span class='hs-keyword'>_</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LMin</span>
<a name="line-136"></a><span class='hs-definition'>intersectRect</span> <span class='hs-keyword'>_</span> <span class='hs-conid'>LMin</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LMin</span>
<a name="line-137"></a><span class='hs-definition'>intersectRect</span> <span class='hs-layout'>(</span><span class='hs-conid'>LValue</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rect</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x11</span> <span class='hs-varid'>y11</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x12</span> <span class='hs-varid'>y12</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span>
<a name="line-138"></a>              <span class='hs-layout'>(</span><span class='hs-conid'>LValue</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rect</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x21</span> <span class='hs-varid'>y21</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x22</span> <span class='hs-varid'>y22</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-139"></a>  <span class='hs-keyword'>let</span> <span class='hs-varid'>p1</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Point</span> <span class='hs-layout'>(</span><span class='hs-varid'>max</span> <span class='hs-varid'>x11</span> <span class='hs-varid'>x21</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>max</span> <span class='hs-varid'>y11</span> <span class='hs-varid'>y21</span><span class='hs-layout'>)</span>
<a name="line-140"></a>      <span class='hs-varid'>p2</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Point</span> <span class='hs-layout'>(</span><span class='hs-varid'>min</span> <span class='hs-varid'>x12</span> <span class='hs-varid'>x22</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>min</span> <span class='hs-varid'>y12</span> <span class='hs-varid'>y22</span><span class='hs-layout'>)</span>
<a name="line-141"></a>  <span class='hs-keyword'>in</span> <span class='hs-keyword'>if</span> <span class='hs-varid'>x2</span> <span class='hs-varop'>&lt;</span> <span class='hs-varid'>x1</span> <span class='hs-varop'>||</span> <span class='hs-varid'>y2</span> <span class='hs-varop'>&lt;</span> <span class='hs-varid'>y1</span>
<a name="line-142"></a>        <span class='hs-keyword'>then</span> <span class='hs-conid'>LMin</span>
<a name="line-143"></a>        <span class='hs-keyword'>else</span> <span class='hs-conid'>LValue</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Rect</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span>
<a name="line-144"></a>
<a name="line-145"></a><a name="Range"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>Range</span>    <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Double</span><span class='hs-layout'>,</span><span class='hs-conid'>Double</span><span class='hs-layout'>)</span>
<a name="line-146"></a><a name="RectSize"></a><span class='hs-keyword'>type</span> <span class='hs-conid'>RectSize</span> <span class='hs-keyglyph'>=</span> <span class='hs-layout'>(</span><span class='hs-conid'>Double</span><span class='hs-layout'>,</span><span class='hs-conid'>Double</span><span class='hs-layout'>)</span>
<a name="line-147"></a>
<a name="line-148"></a><span class='hs-comment'>{-
<a name="line-149"></a>-- | Make a path from a rectangle.
<a name="line-150"></a>rectPointPath :: Rect -&gt; [Point]
<a name="line-151"></a>rectPointPath (Rect p1@(Point x1 y1) p3@(Point x2 y2)) = [p1,p2,p3,p4,p1]
<a name="line-152"></a>  where
<a name="line-153"></a>    p2 = (Point x1 y2)
<a name="line-154"></a>    p4 = (Point x2 y1)
<a name="line-155"></a>-}</span>
<a name="line-156"></a>
<a name="line-157"></a><a name="rectPath"></a><span class='hs-comment'>-- | Make a path from a rectangle.</span>
<a name="line-158"></a><span class='hs-definition'>rectPath</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Rect</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-159"></a><span class='hs-definition'>rectPath</span> <span class='hs-layout'>(</span><span class='hs-conid'>Rect</span> <span class='hs-varid'>p1</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y1</span><span class='hs-layout'>)</span> <span class='hs-varid'>p3</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y2</span><span class='hs-layout'>)</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-160"></a>  <span class='hs-keyword'>let</span> <span class='hs-varid'>p2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Point</span> <span class='hs-varid'>x1</span> <span class='hs-varid'>y2</span>
<a name="line-161"></a>      <span class='hs-varid'>p4</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Point</span> <span class='hs-varid'>x2</span> <span class='hs-varid'>y1</span>
<a name="line-162"></a>  <span class='hs-keyword'>in</span> <span class='hs-varid'>moveTo</span> <span class='hs-varid'>p1</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>lineTo</span> <span class='hs-varid'>p2</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>lineTo</span> <span class='hs-varid'>p3</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>lineTo</span> <span class='hs-varid'>p4</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>close</span>
<a name="line-163"></a>
<a name="line-164"></a><span class='hs-comment'>-- -----------------------------------------------------------------------</span>
<a name="line-165"></a><span class='hs-comment'>-- Path Types</span>
<a name="line-166"></a><span class='hs-comment'>-- -----------------------------------------------------------------------</span>
<a name="line-167"></a>
<a name="line-168"></a><a name="Path"></a><span class='hs-comment'>-- | The path type used by Charts.</span>
<a name="line-169"></a><a name="Path"></a><span class='hs-comment'>--</span>
<a name="line-170"></a><a name="Path"></a><span class='hs-comment'>--   A path can consist of several subpaths. Each</span>
<a name="line-171"></a><a name="Path"></a><span class='hs-comment'>--   is started by a 'MoveTo' operation. All subpaths</span>
<a name="line-172"></a><a name="Path"></a><span class='hs-comment'>--   are open, except the last one, which may be closed</span>
<a name="line-173"></a><a name="Path"></a><span class='hs-comment'>--   using the 'Close' operation. When filling a path</span>
<a name="line-174"></a><a name="Path"></a><span class='hs-comment'>--   all subpaths are closed implicitly.</span>
<a name="line-175"></a><a name="Path"></a><span class='hs-comment'>--</span>
<a name="line-176"></a><a name="Path"></a><span class='hs-comment'>--   Closing a subpath means that a line is drawn from</span>
<a name="line-177"></a><a name="Path"></a><span class='hs-comment'>--   the end point to the start point of the subpath.</span>
<a name="line-178"></a><a name="Path"></a><span class='hs-comment'>--</span>
<a name="line-179"></a><a name="Path"></a><span class='hs-comment'>--   If a 'Arc' (or 'ArcNeg') is drawn a implicit line</span>
<a name="line-180"></a><a name="Path"></a><span class='hs-comment'>--   from the last end point of the subpath is drawn</span>
<a name="line-181"></a><a name="Path"></a><span class='hs-comment'>--   to the beginning of the arc. Another implicit line</span>
<a name="line-182"></a><a name="Path"></a><span class='hs-comment'>--   is drawn from the end of an arc to the beginning of</span>
<a name="line-183"></a><a name="Path"></a><span class='hs-comment'>--   the next path segment.</span>
<a name="line-184"></a><a name="Path"></a><span class='hs-comment'>--</span>
<a name="line-185"></a><a name="Path"></a><span class='hs-comment'>--   The beginning of a subpath is either (0,0) or set</span>
<a name="line-186"></a><a name="Path"></a><span class='hs-comment'>--   by a 'MoveTo' instruction. If the first subpath is started</span>
<a name="line-187"></a><a name="Path"></a><span class='hs-comment'>--   with an arc the beginning of that subpath is the beginning</span>
<a name="line-188"></a><a name="Path"></a><span class='hs-comment'>--   of the arc.</span>
<a name="line-189"></a><a name="Path"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Path</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>MoveTo</span> <span class='hs-conid'>Point</span> <span class='hs-conid'>Path</span>
<a name="line-190"></a>          <span class='hs-keyglyph'>|</span> <span class='hs-conid'>LineTo</span> <span class='hs-conid'>Point</span> <span class='hs-conid'>Path</span>
<a name="line-191"></a>          <span class='hs-keyglyph'>|</span> <span class='hs-conid'>Arc</span> <span class='hs-conid'>Point</span> <span class='hs-conid'>Double</span> <span class='hs-conid'>Double</span> <span class='hs-conid'>Double</span> <span class='hs-conid'>Path</span>
<a name="line-192"></a>          <span class='hs-keyglyph'>|</span> <span class='hs-conid'>ArcNeg</span> <span class='hs-conid'>Point</span> <span class='hs-conid'>Double</span> <span class='hs-conid'>Double</span> <span class='hs-conid'>Double</span> <span class='hs-conid'>Path</span>
<a name="line-193"></a>          <span class='hs-keyglyph'>|</span> <span class='hs-conid'>End</span>
<a name="line-194"></a>          <span class='hs-keyglyph'>|</span> <span class='hs-conid'>Close</span>
<a name="line-195"></a>
<a name="line-196"></a><a name="instance%20Monoid%20Path"></a><span class='hs-comment'>-- | Paths are monoids. After a path is closed you can not append</span>
<a name="line-197"></a><a name="instance%20Monoid%20Path"></a><span class='hs-comment'>--   anything to it anymore. The empty path is open.</span>
<a name="line-198"></a><a name="instance%20Monoid%20Path"></a><span class='hs-comment'>--   Use 'close' to close a path.</span>
<a name="line-199"></a><a name="instance%20Monoid%20Path"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Monoid</span> <span class='hs-conid'>Path</span> <span class='hs-keyword'>where</span>
<a name="line-200"></a>  <span class='hs-varid'>mappend</span> <span class='hs-varid'>p1</span> <span class='hs-varid'>p2</span> <span class='hs-keyglyph'>=</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>p1</span> <span class='hs-keyword'>of</span>
<a name="line-201"></a>    <span class='hs-conid'>MoveTo</span> <span class='hs-varid'>p</span> <span class='hs-varid'>path</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>MoveTo</span> <span class='hs-varid'>p</span> <span class='hs-varop'>$</span> <span class='hs-varid'>mappend</span> <span class='hs-varid'>path</span> <span class='hs-varid'>p2</span>
<a name="line-202"></a>    <span class='hs-conid'>LineTo</span> <span class='hs-varid'>p</span> <span class='hs-varid'>path</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>LineTo</span> <span class='hs-varid'>p</span> <span class='hs-varop'>$</span> <span class='hs-varid'>mappend</span> <span class='hs-varid'>path</span> <span class='hs-varid'>p2</span>
<a name="line-203"></a>    <span class='hs-conid'>Arc</span>    <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varid'>path</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Arc</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varop'>$</span> <span class='hs-varid'>mappend</span> <span class='hs-varid'>path</span> <span class='hs-varid'>p2</span>
<a name="line-204"></a>    <span class='hs-conid'>ArcNeg</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varid'>path</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>ArcNeg</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varop'>$</span> <span class='hs-varid'>mappend</span> <span class='hs-varid'>path</span> <span class='hs-varid'>p2</span>
<a name="line-205"></a>    <span class='hs-conid'>End</span>   <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>p2</span>
<a name="line-206"></a>    <span class='hs-conid'>Close</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Close</span>
<a name="line-207"></a>  <span class='hs-varid'>mempty</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>End</span>
<a name="line-208"></a>
<a name="line-209"></a><a name="moveTo"></a><span class='hs-comment'>-- | Move the paths pointer to the given location.</span>
<a name="line-210"></a><span class='hs-definition'>moveTo</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-211"></a><span class='hs-definition'>moveTo</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>MoveTo</span> <span class='hs-varid'>p</span> <span class='hs-varid'>mempty</span>
<a name="line-212"></a>
<a name="line-213"></a><a name="moveTo'"></a><span class='hs-comment'>-- | Short-cut for 'moveTo', if you don't want to create a 'Point'.</span>
<a name="line-214"></a><span class='hs-definition'>moveTo'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-215"></a><span class='hs-definition'>moveTo'</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>moveTo</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Point</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span>
<a name="line-216"></a>
<a name="line-217"></a><a name="lineTo"></a><span class='hs-comment'>-- | Move the paths pointer to the given location and draw a straight</span>
<a name="line-218"></a><span class='hs-comment'>--   line while doing so.</span>
<a name="line-219"></a><span class='hs-definition'>lineTo</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-220"></a><span class='hs-definition'>lineTo</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>LineTo</span> <span class='hs-varid'>p</span> <span class='hs-varid'>mempty</span>
<a name="line-221"></a>
<a name="line-222"></a><a name="lineTo'"></a><span class='hs-comment'>-- | Short-cut for 'lineTo', if you don't want to create a 'Point'.</span>
<a name="line-223"></a><span class='hs-definition'>lineTo'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-224"></a><span class='hs-definition'>lineTo'</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>lineTo</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Point</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span>
<a name="line-225"></a>
<a name="line-226"></a><a name="arc"></a><span class='hs-comment'>-- | Draw the arc of a circle. A straight line connects</span>
<a name="line-227"></a><span class='hs-comment'>--   the end of the previous path with the beginning of the arc.</span>
<a name="line-228"></a><span class='hs-comment'>--   The zero angle points in direction of the positive x-axis.</span>
<a name="line-229"></a><span class='hs-comment'>--   Angles increase in clock-wise direction. If the stop angle</span>
<a name="line-230"></a><span class='hs-comment'>--   is smaller then the start angle it is increased by multiples of</span>
<a name="line-231"></a><span class='hs-comment'>--   @2 * pi@ until is is greater or equal.</span>
<a name="line-232"></a><span class='hs-definition'>arc</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span>  <span class='hs-comment'>-- ^ Center point of the circle arc.</span>
<a name="line-233"></a>    <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-comment'>-- ^ Radius of the circle.</span>
<a name="line-234"></a>    <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-comment'>-- ^ Angle to start drawing at, in radians.</span>
<a name="line-235"></a>    <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-comment'>-- ^ Angle to stop drawing at, in radians.</span>
<a name="line-236"></a>    <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-237"></a><span class='hs-definition'>arc</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Arc</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varid'>mempty</span>
<a name="line-238"></a>
<a name="line-239"></a><a name="arc'"></a><span class='hs-comment'>-- | Short-cut for 'arc', if you don't want to create a 'Point'.</span>
<a name="line-240"></a><span class='hs-definition'>arc'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-241"></a><span class='hs-definition'>arc'</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Arc</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varid'>mempty</span>
<a name="line-242"></a>
<a name="line-243"></a><a name="arcNeg"></a><span class='hs-comment'>-- | Like 'arc', but draws from the stop angle to the start angle</span>
<a name="line-244"></a><span class='hs-comment'>--   instead of between them.</span>
<a name="line-245"></a><span class='hs-definition'>arcNeg</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-246"></a><span class='hs-definition'>arcNeg</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ArcNeg</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varid'>mempty</span>
<a name="line-247"></a>
<a name="line-248"></a><a name="arcNeg'"></a><span class='hs-comment'>-- | Short-cut for 'arcNeg', if you don't want to create a 'Point'.</span>
<a name="line-249"></a><span class='hs-definition'>arcNeg'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-250"></a><span class='hs-definition'>arcNeg'</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>ArcNeg</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varid'>mempty</span>
<a name="line-251"></a>
<a name="line-252"></a><a name="close"></a><span class='hs-comment'>-- | A closed empty path. Closes a path when appended.</span>
<a name="line-253"></a><span class='hs-definition'>close</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Path</span>
<a name="line-254"></a><span class='hs-definition'>close</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Close</span>
<a name="line-255"></a>
<a name="line-256"></a><a name="foldPath"></a><span class='hs-comment'>-- | Fold the given path to a monoid structure.</span>
<a name="line-257"></a><span class='hs-definition'>foldPath</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Monoid</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span>
<a name="line-258"></a>         <span class='hs-keyglyph'>=&gt;</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- ^ MoveTo</span>
<a name="line-259"></a>         <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- ^ LineTo</span>
<a name="line-260"></a>         <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- ^ Arc</span>
<a name="line-261"></a>         <span class='hs-keyglyph'>-&gt;</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span><span class='hs-layout'>)</span> <span class='hs-comment'>-- ^ ArcNeg</span>
<a name="line-262"></a>         <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span>    <span class='hs-comment'>-- ^ Close</span>
<a name="line-263"></a>         <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span> <span class='hs-comment'>-- ^ Path to fold</span>
<a name="line-264"></a>         <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>m</span>
<a name="line-265"></a><span class='hs-definition'>foldPath</span> <span class='hs-varid'>moveTo_</span> <span class='hs-varid'>lineTo_</span> <span class='hs-varid'>arc_</span> <span class='hs-varid'>arcNeg_</span> <span class='hs-varid'>close_</span> <span class='hs-varid'>path</span> <span class='hs-keyglyph'>=</span>
<a name="line-266"></a>  <span class='hs-keyword'>let</span> <span class='hs-varid'>restF</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>foldPath</span> <span class='hs-varid'>moveTo_</span> <span class='hs-varid'>lineTo_</span> <span class='hs-varid'>arc_</span> <span class='hs-varid'>arcNeg_</span> <span class='hs-varid'>close_</span>
<a name="line-267"></a>  <span class='hs-keyword'>in</span> <span class='hs-keyword'>case</span> <span class='hs-varid'>path</span> <span class='hs-keyword'>of</span>
<a name="line-268"></a>    <span class='hs-conid'>MoveTo</span> <span class='hs-varid'>p</span> <span class='hs-varid'>rest</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>moveTo_</span> <span class='hs-varid'>p</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>restF</span> <span class='hs-varid'>rest</span>
<a name="line-269"></a>    <span class='hs-conid'>LineTo</span> <span class='hs-varid'>p</span> <span class='hs-varid'>rest</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>lineTo_</span> <span class='hs-varid'>p</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>restF</span> <span class='hs-varid'>rest</span>
<a name="line-270"></a>    <span class='hs-conid'>Arc</span>    <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varid'>rest</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>arc_</span>    <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>restF</span> <span class='hs-varid'>rest</span>
<a name="line-271"></a>    <span class='hs-conid'>ArcNeg</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varid'>rest</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>arcNeg_</span> <span class='hs-varid'>p</span> <span class='hs-varid'>r</span> <span class='hs-varid'>a1</span> <span class='hs-varid'>a2</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>restF</span> <span class='hs-varid'>rest</span>
<a name="line-272"></a>    <span class='hs-conid'>End</span>   <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>mempty</span>
<a name="line-273"></a>    <span class='hs-conid'>Close</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-varid'>close_</span>
<a name="line-274"></a>
<a name="line-275"></a><a name="makeLinesExplicit"></a><span class='hs-comment'>-- | Enriches the path with explicit instructions to draw lines,</span>
<a name="line-276"></a><span class='hs-comment'>--   that otherwise would be implicit. See 'Path' for details</span>
<a name="line-277"></a><span class='hs-comment'>--   about what lines in paths are implicit.</span>
<a name="line-278"></a><span class='hs-definition'>makeLinesExplicit</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Path</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-279"></a><span class='hs-definition'>makeLinesExplicit</span> <span class='hs-layout'>(</span><span class='hs-conid'>Arc</span> <span class='hs-varid'>c</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-280"></a>  <span class='hs-conid'>Arc</span> <span class='hs-varid'>c</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span> <span class='hs-varop'>$</span> <span class='hs-varid'>makeLinesExplicit'</span> <span class='hs-varid'>rest</span>
<a name="line-281"></a><span class='hs-definition'>makeLinesExplicit</span> <span class='hs-layout'>(</span><span class='hs-conid'>ArcNeg</span> <span class='hs-varid'>c</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-282"></a>  <span class='hs-conid'>ArcNeg</span> <span class='hs-varid'>c</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span> <span class='hs-varop'>$</span> <span class='hs-varid'>makeLinesExplicit'</span> <span class='hs-varid'>rest</span>
<a name="line-283"></a><span class='hs-definition'>makeLinesExplicit</span> <span class='hs-varid'>path</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>makeLinesExplicit'</span> <span class='hs-varid'>path</span>
<a name="line-284"></a>
<a name="line-285"></a><a name="makeLinesExplicit'"></a><span class='hs-comment'>-- | Utility for 'makeLinesExplicit'.</span>
<a name="line-286"></a><span class='hs-definition'>makeLinesExplicit'</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Path</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Path</span>
<a name="line-287"></a><span class='hs-definition'>makeLinesExplicit'</span> <span class='hs-conid'>End</span>   <span class='hs-keyglyph'>=</span> <span class='hs-conid'>End</span>
<a name="line-288"></a><span class='hs-definition'>makeLinesExplicit'</span> <span class='hs-conid'>Close</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Close</span>
<a name="line-289"></a><span class='hs-definition'>makeLinesExplicit'</span> <span class='hs-layout'>(</span><span class='hs-conid'>Arc</span> <span class='hs-varid'>c</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-290"></a>  <span class='hs-keyword'>let</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>translateP</span> <span class='hs-layout'>(</span><span class='hs-varid'>pointToVec</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>rotateP</span> <span class='hs-varid'>s</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Point</span> <span class='hs-varid'>r</span> <span class='hs-num'>0</span>
<a name="line-291"></a>  <span class='hs-keyword'>in</span> <span class='hs-varid'>lineTo</span> <span class='hs-varid'>p</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>arc</span> <span class='hs-varid'>c</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>makeLinesExplicit'</span> <span class='hs-varid'>rest</span>
<a name="line-292"></a><span class='hs-definition'>makeLinesExplicit'</span> <span class='hs-layout'>(</span><span class='hs-conid'>ArcNeg</span> <span class='hs-varid'>c</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-293"></a>  <span class='hs-keyword'>let</span> <span class='hs-varid'>p</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>translateP</span> <span class='hs-layout'>(</span><span class='hs-varid'>pointToVec</span> <span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>rotateP</span> <span class='hs-varid'>s</span> <span class='hs-varop'>$</span> <span class='hs-conid'>Point</span> <span class='hs-varid'>r</span> <span class='hs-num'>0</span>
<a name="line-294"></a>  <span class='hs-keyword'>in</span> <span class='hs-varid'>lineTo</span> <span class='hs-varid'>p</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>arcNeg</span> <span class='hs-varid'>c</span> <span class='hs-varid'>r</span> <span class='hs-varid'>s</span> <span class='hs-varid'>e</span> <span class='hs-varop'>&lt;&gt;</span> <span class='hs-varid'>makeLinesExplicit'</span> <span class='hs-varid'>rest</span>
<a name="line-295"></a><span class='hs-definition'>makeLinesExplicit'</span> <span class='hs-layout'>(</span><span class='hs-conid'>MoveTo</span> <span class='hs-varid'>p0</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-296"></a>  <span class='hs-conid'>MoveTo</span> <span class='hs-varid'>p0</span> <span class='hs-varop'>$</span> <span class='hs-varid'>makeLinesExplicit'</span> <span class='hs-varid'>rest</span>
<a name="line-297"></a><span class='hs-definition'>makeLinesExplicit'</span> <span class='hs-layout'>(</span><span class='hs-conid'>LineTo</span> <span class='hs-varid'>p0</span> <span class='hs-varid'>rest</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-298"></a>  <span class='hs-conid'>LineTo</span> <span class='hs-varid'>p0</span> <span class='hs-varop'>$</span> <span class='hs-varid'>makeLinesExplicit'</span> <span class='hs-varid'>rest</span>
<a name="line-299"></a>
<a name="line-300"></a><span class='hs-comment'>-- -----------------------------------------------------------------------</span>
<a name="line-301"></a><span class='hs-comment'>-- Matrix Type</span>
<a name="line-302"></a><span class='hs-comment'>-- -----------------------------------------------------------------------</span>
<a name="line-303"></a>
<a name="line-304"></a><a name="transformP"></a><span class='hs-comment'>-- | Transform a point using the given matrix.</span>
<a name="line-305"></a><span class='hs-definition'>transformP</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span>
<a name="line-306"></a><span class='hs-definition'>transformP</span> <span class='hs-varid'>t</span> <span class='hs-layout'>(</span><span class='hs-conid'>Point</span> <span class='hs-varid'>x</span> <span class='hs-varid'>y</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Point</span>
<a name="line-307"></a>  <span class='hs-layout'>(</span><span class='hs-varid'>xx</span> <span class='hs-varid'>t</span> <span class='hs-varop'>*</span> <span class='hs-varid'>x</span> <span class='hs-varop'>+</span> <span class='hs-varid'>xy</span> <span class='hs-varid'>t</span> <span class='hs-varop'>*</span> <span class='hs-varid'>y</span> <span class='hs-varop'>+</span> <span class='hs-varid'>x0</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<a name="line-308"></a>  <span class='hs-layout'>(</span><span class='hs-varid'>yx</span> <span class='hs-varid'>t</span> <span class='hs-varop'>*</span> <span class='hs-varid'>x</span> <span class='hs-varop'>+</span> <span class='hs-varid'>yy</span> <span class='hs-varid'>t</span> <span class='hs-varop'>*</span> <span class='hs-varid'>y</span> <span class='hs-varop'>+</span> <span class='hs-varid'>y0</span> <span class='hs-varid'>t</span><span class='hs-layout'>)</span>
<a name="line-309"></a>
<a name="line-310"></a><a name="rotateP"></a><span class='hs-comment'>-- | Rotate a point around the origin.</span>
<a name="line-311"></a><span class='hs-comment'>--   The angle is given in radians.</span>
<a name="line-312"></a><span class='hs-definition'>rotateP</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span>
<a name="line-313"></a><span class='hs-definition'>rotateP</span> <span class='hs-varid'>a</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transformP</span> <span class='hs-layout'>(</span><span class='hs-varid'>rotate</span> <span class='hs-varid'>a</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-314"></a>
<a name="line-315"></a><a name="scaleP"></a><span class='hs-comment'>-- | Scale a point.</span>
<a name="line-316"></a><span class='hs-definition'>scaleP</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span>
<a name="line-317"></a><span class='hs-definition'>scaleP</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>transformP</span> <span class='hs-layout'>(</span><span class='hs-varid'>scale</span> <span class='hs-varid'>s</span> <span class='hs-num'>1</span><span class='hs-layout'>)</span>
<a name="line-318"></a>
<a name="line-319"></a><a name="translateP"></a><span class='hs-comment'>-- | Translate a point.</span>
<a name="line-320"></a><span class='hs-definition'>translateP</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Point</span>
<a name="line-321"></a><span class='hs-definition'>translateP</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>flip</span> <span class='hs-varid'>pvadd</span>
<a name="line-322"></a>
<a name="line-323"></a><a name="Matrix"></a><span class='hs-comment'>-- | Copied from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-324"></a><a name="Matrix"></a><span class='hs-keyword'>data</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Matrix</span> <span class='hs-layout'>{</span> <span class='hs-varid'>xx</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-conid'>Double</span><span class='hs-layout'>,</span> <span class='hs-varid'>yx</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-conid'>Double</span><span class='hs-layout'>,</span>
<a name="line-325"></a>                       <span class='hs-varid'>xy</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-conid'>Double</span><span class='hs-layout'>,</span> <span class='hs-varid'>yy</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-conid'>Double</span><span class='hs-layout'>,</span>
<a name="line-326"></a>                       <span class='hs-varid'>x0</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-conid'>Double</span><span class='hs-layout'>,</span> <span class='hs-varid'>y0</span> <span class='hs-keyglyph'>::</span> <span class='hs-varop'>!</span><span class='hs-conid'>Double</span> <span class='hs-layout'>}</span>
<a name="line-327"></a>                     <span class='hs-keyword'>deriving</span> <span class='hs-conid'>Show</span>
<a name="line-328"></a>
<a name="line-329"></a><a name="instance%20Num%20Matrix"></a><span class='hs-comment'>-- | Copied from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-330"></a><a name="instance%20Num%20Matrix"></a><span class='hs-keyword'>instance</span> <span class='hs-conid'>Num</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyword'>where</span>
<a name="line-331"></a>  <span class='hs-comment'>-- use underscore to avoid ghc complaints about shadowing the Matrix</span>
<a name="line-332"></a>  <span class='hs-comment'>-- field names</span>
<a name="line-333"></a>  <span class='hs-layout'>(</span><span class='hs-varop'>*</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Matrix</span> <span class='hs-varid'>xx_</span> <span class='hs-varid'>yx_</span> <span class='hs-varid'>xy_</span> <span class='hs-varid'>yy_</span> <span class='hs-varid'>x0_</span> <span class='hs-varid'>y0_</span><span class='hs-layout'>)</span>
<a name="line-334"></a>      <span class='hs-layout'>(</span><span class='hs-conid'>Matrix</span> <span class='hs-varid'>xx'_</span> <span class='hs-varid'>yx'_</span> <span class='hs-varid'>xy'_</span> <span class='hs-varid'>yy'_</span> <span class='hs-varid'>x0'_</span> <span class='hs-varid'>y0'_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-335"></a>    <span class='hs-conid'>Matrix</span> <span class='hs-layout'>(</span><span class='hs-varid'>xx_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>xx'_</span> <span class='hs-varop'>+</span> <span class='hs-varid'>yx_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>xy'_</span><span class='hs-layout'>)</span>
<a name="line-336"></a>           <span class='hs-layout'>(</span><span class='hs-varid'>xx_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>yx'_</span> <span class='hs-varop'>+</span> <span class='hs-varid'>yx_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>yy'_</span><span class='hs-layout'>)</span>
<a name="line-337"></a>           <span class='hs-layout'>(</span><span class='hs-varid'>xy_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>xx'_</span> <span class='hs-varop'>+</span> <span class='hs-varid'>yy_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>xy'_</span><span class='hs-layout'>)</span>
<a name="line-338"></a>           <span class='hs-layout'>(</span><span class='hs-varid'>xy_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>yx'_</span> <span class='hs-varop'>+</span> <span class='hs-varid'>yy_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>yy'_</span><span class='hs-layout'>)</span>
<a name="line-339"></a>           <span class='hs-layout'>(</span><span class='hs-varid'>x0_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>xx'_</span> <span class='hs-varop'>+</span> <span class='hs-varid'>y0_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>xy'_</span> <span class='hs-varop'>+</span> <span class='hs-varid'>x0'_</span><span class='hs-layout'>)</span>
<a name="line-340"></a>           <span class='hs-layout'>(</span><span class='hs-varid'>x0_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>yx'_</span> <span class='hs-varop'>+</span> <span class='hs-varid'>y0_</span> <span class='hs-varop'>*</span> <span class='hs-varid'>yy'_</span> <span class='hs-varop'>+</span> <span class='hs-varid'>y0'_</span><span class='hs-layout'>)</span>
<a name="line-341"></a>
<a name="line-342"></a>  <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pointwise2</span> <span class='hs-layout'>(</span><span class='hs-varop'>+</span><span class='hs-layout'>)</span>
<a name="line-343"></a>  <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pointwise2</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-layout'>)</span>
<a name="line-344"></a>
<a name="line-345"></a>  <span class='hs-varid'>negate</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pointwise</span> <span class='hs-varid'>negate</span>
<a name="line-346"></a>  <span class='hs-varid'>abs</span>    <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pointwise</span> <span class='hs-varid'>abs</span>
<a name="line-347"></a>  <span class='hs-varid'>signum</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pointwise</span> <span class='hs-varid'>signum</span>
<a name="line-348"></a>
<a name="line-349"></a>  <span class='hs-varid'>fromInteger</span> <span class='hs-varid'>n</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Matrix</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromInteger</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span> <span class='hs-layout'>(</span><span class='hs-varid'>fromInteger</span> <span class='hs-varid'>n</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span>
<a name="line-350"></a>
<a name="line-351"></a><a name="pointwise"></a><span class='hs-comment'>-- | Copied from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-352"></a><span class='hs-comment'>{-# INLINE pointwise #-}</span>
<a name="line-353"></a><span class='hs-definition'>pointwise</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span>
<a name="line-354"></a><span class='hs-definition'>pointwise</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Matrix</span> <span class='hs-varid'>xx_</span> <span class='hs-varid'>yx_</span> <span class='hs-varid'>xy_</span> <span class='hs-varid'>yy_</span> <span class='hs-varid'>x0_</span> <span class='hs-varid'>y0_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-355"></a>  <span class='hs-conid'>Matrix</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>xx_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>yx_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>xy_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>yy_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x0_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>y0_</span><span class='hs-layout'>)</span>
<a name="line-356"></a>
<a name="line-357"></a><a name="pointwise2"></a><span class='hs-comment'>-- | Copied from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-358"></a><span class='hs-comment'>{-# INLINE pointwise2 #-}</span>
<a name="line-359"></a><span class='hs-definition'>pointwise2</span> <span class='hs-keyglyph'>::</span> <span class='hs-layout'>(</span><span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Double</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span>
<a name="line-360"></a><span class='hs-definition'>pointwise2</span> <span class='hs-varid'>f</span> <span class='hs-layout'>(</span><span class='hs-conid'>Matrix</span> <span class='hs-varid'>xx_</span> <span class='hs-varid'>yx_</span> <span class='hs-varid'>xy_</span> <span class='hs-varid'>yy_</span> <span class='hs-varid'>x0_</span> <span class='hs-varid'>y0_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-conid'>Matrix</span> <span class='hs-varid'>xx'_</span> <span class='hs-varid'>yx'_</span> <span class='hs-varid'>xy'_</span> <span class='hs-varid'>yy'_</span> <span class='hs-varid'>x0'_</span> <span class='hs-varid'>y0'_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-361"></a>  <span class='hs-conid'>Matrix</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>xx_</span> <span class='hs-varid'>xx'_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>yx_</span> <span class='hs-varid'>yx'_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>xy_</span> <span class='hs-varid'>xy'_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>yy_</span> <span class='hs-varid'>yy'_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>x0_</span> <span class='hs-varid'>x0'_</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>f</span> <span class='hs-varid'>y0_</span> <span class='hs-varid'>y0'_</span><span class='hs-layout'>)</span>
<a name="line-362"></a>
<a name="line-363"></a><a name="identity"></a><span class='hs-comment'>-- | Copied from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-364"></a><span class='hs-definition'>identity</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Matrix</span>
<a name="line-365"></a><span class='hs-definition'>identity</span> <span class='hs-keyglyph'>=</span> <span class='hs-conid'>Matrix</span> <span class='hs-num'>1</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span> <span class='hs-num'>1</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span>
<a name="line-366"></a>
<a name="line-367"></a><a name="translate"></a><span class='hs-comment'>-- | Copied and adopted from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-368"></a><span class='hs-definition'>translate</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span>
<a name="line-369"></a><span class='hs-definition'>translate</span> <span class='hs-varid'>tv</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>m</span> <span class='hs-varop'>*</span> <span class='hs-conid'>Matrix</span> <span class='hs-num'>1</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span> <span class='hs-num'>1</span> <span class='hs-layout'>(</span><span class='hs-varid'>v_x</span> <span class='hs-varid'>tv</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>v_y</span> <span class='hs-varid'>tv</span><span class='hs-layout'>)</span>
<a name="line-370"></a>
<a name="line-371"></a><a name="scale"></a><span class='hs-comment'>-- | Copied and adopted from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-372"></a><span class='hs-definition'>scale</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Vector</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span>
<a name="line-373"></a><span class='hs-definition'>scale</span> <span class='hs-varid'>sv</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>m</span> <span class='hs-varop'>*</span> <span class='hs-conid'>Matrix</span> <span class='hs-layout'>(</span><span class='hs-varid'>v_x</span> <span class='hs-varid'>sv</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span> <span class='hs-layout'>(</span><span class='hs-varid'>v_y</span> <span class='hs-varid'>sv</span><span class='hs-layout'>)</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span>
<a name="line-374"></a>
<a name="line-375"></a><a name="rotate"></a><span class='hs-comment'>-- | Copied from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-376"></a><span class='hs-comment'>--   Rotations angle is given in radians.</span>
<a name="line-377"></a><span class='hs-definition'>rotate</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span>
<a name="line-378"></a><span class='hs-definition'>rotate</span> <span class='hs-varid'>r</span> <span class='hs-varid'>m</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>m</span> <span class='hs-varop'>*</span> <span class='hs-conid'>Matrix</span> <span class='hs-varid'>c</span> <span class='hs-varid'>s</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>s</span><span class='hs-layout'>)</span> <span class='hs-varid'>c</span> <span class='hs-num'>0</span> <span class='hs-num'>0</span>
<a name="line-379"></a>  <span class='hs-keyword'>where</span> <span class='hs-varid'>s</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>sin</span> <span class='hs-varid'>r</span>
<a name="line-380"></a>        <span class='hs-varid'>c</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>cos</span> <span class='hs-varid'>r</span>
<a name="line-381"></a>
<a name="line-382"></a><a name="scalarMultiply"></a><span class='hs-comment'>-- | Copied from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-383"></a><span class='hs-definition'>scalarMultiply</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Double</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span>
<a name="line-384"></a><span class='hs-definition'>scalarMultiply</span> <span class='hs-varid'>scalar</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>pointwise</span> <span class='hs-layout'>(</span><span class='hs-varop'>*</span> <span class='hs-varid'>scalar</span><span class='hs-layout'>)</span>
<a name="line-385"></a>
<a name="line-386"></a><a name="adjoint"></a><span class='hs-comment'>-- | Copied from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-387"></a><span class='hs-definition'>adjoint</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span>
<a name="line-388"></a><span class='hs-definition'>adjoint</span> <span class='hs-layout'>(</span><span class='hs-conid'>Matrix</span> <span class='hs-varid'>a</span> <span class='hs-varid'>b</span> <span class='hs-varid'>c</span> <span class='hs-varid'>d</span> <span class='hs-varid'>tx</span> <span class='hs-varid'>ty</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span>
<a name="line-389"></a>  <span class='hs-conid'>Matrix</span> <span class='hs-varid'>d</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>b</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-comment'>-</span><span class='hs-varid'>c</span><span class='hs-layout'>)</span> <span class='hs-varid'>a</span> <span class='hs-layout'>(</span><span class='hs-varid'>c</span><span class='hs-varop'>*</span><span class='hs-varid'>ty</span> <span class='hs-comment'>-</span> <span class='hs-varid'>d</span><span class='hs-varop'>*</span><span class='hs-varid'>tx</span><span class='hs-layout'>)</span> <span class='hs-layout'>(</span><span class='hs-varid'>b</span><span class='hs-varop'>*</span><span class='hs-varid'>tx</span> <span class='hs-comment'>-</span> <span class='hs-varid'>a</span><span class='hs-varop'>*</span><span class='hs-varid'>ty</span><span class='hs-layout'>)</span>
<a name="line-390"></a>
<a name="line-391"></a><a name="invert"></a><span class='hs-comment'>-- | Copied from Graphics.Rendering.Cairo.Matrix</span>
<a name="line-392"></a><span class='hs-definition'>invert</span> <span class='hs-keyglyph'>::</span> <span class='hs-conid'>Matrix</span> <span class='hs-keyglyph'>-&gt;</span> <span class='hs-conid'>Matrix</span>
<a name="line-393"></a><span class='hs-definition'>invert</span> <span class='hs-varid'>m</span><span class='hs-keyglyph'>@</span><span class='hs-layout'>(</span><span class='hs-conid'>Matrix</span> <span class='hs-varid'>xx_</span> <span class='hs-varid'>yx_</span> <span class='hs-varid'>xy_</span> <span class='hs-varid'>yy_</span> <span class='hs-keyword'>_</span> <span class='hs-keyword'>_</span><span class='hs-layout'>)</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>scalarMultiply</span> <span class='hs-layout'>(</span><span class='hs-varid'>recip</span> <span class='hs-varid'>det</span><span class='hs-layout'>)</span> <span class='hs-varop'>$</span> <span class='hs-varid'>adjoint</span> <span class='hs-varid'>m</span>
<a name="line-394"></a>  <span class='hs-keyword'>where</span> <span class='hs-varid'>det</span> <span class='hs-keyglyph'>=</span> <span class='hs-varid'>xx_</span><span class='hs-varop'>*</span><span class='hs-varid'>yy_</span> <span class='hs-comment'>-</span> <span class='hs-varid'>yx_</span><span class='hs-varop'>*</span><span class='hs-varid'>xy_</span>
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