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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
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   <div id="projectname">CMU462 Library
   &#160;<span id="projectnumber">1.0</span>
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   <div id="projectbrief">15-462/15-662: Computer Graphics (Fall 2015)</div>
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<li class="navelem"><a class="el" href="dir_d44c64559bbebec7f509842c48db8b23.html">include</a></li><li class="navelem"><a class="el" href="dir_93cde9e1f49b119e2b24d2ae2dcc682a.html">CMU462</a></li>  </ul>
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<div class="title">vector2D.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef CMU462_VECTOR2D_H</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor">#define CMU462_VECTOR2D_H</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;</div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &quot;CMU462.h&quot;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;</div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &lt;ostream&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &lt;cmath&gt;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;</div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespace_c_m_u462.html">CMU462</a> {</div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;</div>
<div class="line"><a name="l00014"></a><span class="lineno"><a class="line" href="class_c_m_u462_1_1_vector2_d.html">   14</a></span>&#160;<span class="keyword">class </span><a class="code" href="class_c_m_u462_1_1_vector2_d.html">Vector2D</a> {</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;</div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;  <span class="comment">// components</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;  <span class="keywordtype">double</span> x, y;</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;</div>
<div class="line"><a name="l00024"></a><span class="lineno"><a class="line" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">   24</a></span>&#160;  <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a>() : x( 0.0 ), y( 0.0 ) { }</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;</div>
<div class="line"><a name="l00030"></a><span class="lineno"><a class="line" href="class_c_m_u462_1_1_vector2_d.html#aca8b0bf43db07df17fb71c1782469819">   30</a></span>&#160;  <a class="code" href="class_c_m_u462_1_1_vector2_d.html#aca8b0bf43db07df17fb71c1782469819">Vector2D</a>( <span class="keywordtype">double</span> x, <span class="keywordtype">double</span> y ) : x( x ), y( y ) { }</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;</div>
<div class="line"><a name="l00036"></a><span class="lineno"><a class="line" href="class_c_m_u462_1_1_vector2_d.html#a37a80c562908c95fb8d9cdc43b17a91d">   36</a></span>&#160;  <a class="code" href="class_c_m_u462_1_1_vector2_d.html#a37a80c562908c95fb8d9cdc43b17a91d">Vector2D</a>( <span class="keyword">const</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html">Vector2D</a>&amp; v ) : x( v.x ), y( v.y ) { }</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  <span class="comment">// additive inverse</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;  <span class="keyword">inline</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html">Vector2D</a> operator-( <span class="keywordtype">void</span> )<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="keywordflow">return</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a>( -x, -y );</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;  }</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;  <span class="comment">// addition</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;  <span class="keyword">inline</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a> operator+( <span class="keyword">const</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a>&amp; v )<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a> u = *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    u += v;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    <span class="keywordflow">return</span> u;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;  }</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  <span class="comment">// subtraction</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  <span class="keyword">inline</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a> operator-( <span class="keyword">const</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a>&amp; v )<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a> u = *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;    u -= v;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;    <span class="keywordflow">return</span> u;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  }</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;  <span class="comment">// right scalar multiplication</span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;  <span class="keyword">inline</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a> operator*( <span class="keywordtype">double</span> r )<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;    <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a> vr = *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;    vr *= r;</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;    <span class="keywordflow">return</span> vr;</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;  }</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  <span class="comment">// scalar division</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  <span class="keyword">inline</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a> operator/( <span class="keywordtype">double</span> r )<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;    <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a> vr = *<span class="keyword">this</span>;</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;    vr /= r;</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keywordflow">return</span> vr;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  }</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  <span class="comment">// add v</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> operator+=( <span class="keyword">const</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a>&amp; v ) {</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    x += v.x;</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;    y += v.y;</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  }</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  <span class="comment">// subtract v</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> operator-=( <span class="keyword">const</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">Vector2D</a>&amp; v ) {</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;    x -= v.x;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;    y -= v.y;</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  }</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  <span class="comment">// scalar multiply by r</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> operator*=( <span class="keywordtype">double</span> r ) {</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    x *= r;</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    y *= r;</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  }</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  <span class="comment">// scalar divide by r</span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">void</span> operator/=( <span class="keywordtype">double</span> r ) {</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    x /= r;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;    y /= r;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;  }</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div>
<div class="line"><a name="l00098"></a><span class="lineno"><a class="line" href="class_c_m_u462_1_1_vector2_d.html#a16553d2c029d5b5274c0fa6837ac259a">   98</a></span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#a16553d2c029d5b5274c0fa6837ac259a">norm</a>( <span class="keywordtype">void</span> )<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;    <span class="keywordflow">return</span> sqrt( x*x + y*y );</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  }</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;</div>
<div class="line"><a name="l00105"></a><span class="lineno"><a class="line" href="class_c_m_u462_1_1_vector2_d.html#a9ac89fa1427ed0ac8019752bd2ff261f">  105</a></span>&#160;  <span class="keyword">inline</span> <span class="keywordtype">double</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#a9ac89fa1427ed0ac8019752bd2ff261f">norm2</a>( <span class="keywordtype">void</span> )<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    <span class="keywordflow">return</span> x*x + y*y;</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  }</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;</div>
<div class="line"><a name="l00112"></a><span class="lineno"><a class="line" href="class_c_m_u462_1_1_vector2_d.html#aecad9e083d41f03929fb01e60851dfa8">  112</a></span>&#160;  <span class="keyword">inline</span> <a class="code" href="class_c_m_u462_1_1_vector2_d.html">Vector2D</a> <a class="code" href="class_c_m_u462_1_1_vector2_d.html#aecad9e083d41f03929fb01e60851dfa8">unit</a>( <span class="keywordtype">void</span> )<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    <span class="keywordflow">return</span> *<span class="keyword">this</span> / this-&gt;<a class="code" href="class_c_m_u462_1_1_vector2_d.html#a16553d2c029d5b5274c0fa6837ac259a">norm</a>();</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  }</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;}; <span class="comment">// clasd Vector2D</span></div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;<span class="comment">// left scalar multiplication</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;<span class="keyword">inline</span> Vector2D operator*( <span class="keywordtype">double</span> r, <span class="keyword">const</span> Vector2D&amp; v ) {</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;   <span class="keywordflow">return</span> v*r;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;}</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="comment">// inner product</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">double</span> dot( <span class="keyword">const</span> Vector2D&amp; v1, <span class="keyword">const</span> Vector2D&amp; v2 ) {</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;  <span class="keywordflow">return</span> v1.x*v2.x + v1.y*v2.y;</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;}</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;<span class="comment">// cross product</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;<span class="keyword">inline</span> <span class="keywordtype">double</span> cross( <span class="keyword">const</span> Vector2D&amp; v1, <span class="keyword">const</span> Vector2D&amp; v2 ) {</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  <span class="keywordflow">return</span> v1.x*v2.y - v1.y*v2.x;</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;}</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;<span class="comment">// prints components</span></div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;std::ostream&amp; operator&lt;&lt;( std::ostream&amp; os, <span class="keyword">const</span> Vector2D&amp; v );</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;} <span class="comment">// namespace CMU462</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;<span class="preprocessor">#endif // CMU462_VECTOR2D_H</span></div>
<div class="ttc" id="class_c_m_u462_1_1_vector2_d_html_ad594e740a756ef6d4e494d65120d2664"><div class="ttname"><a href="class_c_m_u462_1_1_vector2_d.html#ad594e740a756ef6d4e494d65120d2664">CMU462::Vector2D::Vector2D</a></div><div class="ttdeci">Vector2D()</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> vector2D.h:24</div></div>
<div class="ttc" id="class_c_m_u462_1_1_vector2_d_html_a9ac89fa1427ed0ac8019752bd2ff261f"><div class="ttname"><a href="class_c_m_u462_1_1_vector2_d.html#a9ac89fa1427ed0ac8019752bd2ff261f">CMU462::Vector2D::norm2</a></div><div class="ttdeci">double norm2(void) const </div><div class="ttdoc">Returns norm squared. </div><div class="ttdef"><b>Definition:</b> vector2D.h:105</div></div>
<div class="ttc" id="class_c_m_u462_1_1_vector2_d_html_a16553d2c029d5b5274c0fa6837ac259a"><div class="ttname"><a href="class_c_m_u462_1_1_vector2_d.html#a16553d2c029d5b5274c0fa6837ac259a">CMU462::Vector2D::norm</a></div><div class="ttdeci">double norm(void) const </div><div class="ttdoc">Returns norm. </div><div class="ttdef"><b>Definition:</b> vector2D.h:98</div></div>
<div class="ttc" id="class_c_m_u462_1_1_vector2_d_html_aca8b0bf43db07df17fb71c1782469819"><div class="ttname"><a href="class_c_m_u462_1_1_vector2_d.html#aca8b0bf43db07df17fb71c1782469819">CMU462::Vector2D::Vector2D</a></div><div class="ttdeci">Vector2D(double x, double y)</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> vector2D.h:30</div></div>
<div class="ttc" id="namespace_c_m_u462_html"><div class="ttname"><a href="namespace_c_m_u462.html">CMU462</a></div><div class="ttdef"><b>Definition:</b> CMU462.h:8</div></div>
<div class="ttc" id="class_c_m_u462_1_1_vector2_d_html"><div class="ttname"><a href="class_c_m_u462_1_1_vector2_d.html">CMU462::Vector2D</a></div><div class="ttdoc">Defines 2D vectors. </div><div class="ttdef"><b>Definition:</b> vector2D.h:14</div></div>
<div class="ttc" id="class_c_m_u462_1_1_vector2_d_html_a37a80c562908c95fb8d9cdc43b17a91d"><div class="ttname"><a href="class_c_m_u462_1_1_vector2_d.html#a37a80c562908c95fb8d9cdc43b17a91d">CMU462::Vector2D::Vector2D</a></div><div class="ttdeci">Vector2D(const Vector2D &amp;v)</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> vector2D.h:36</div></div>
<div class="ttc" id="class_c_m_u462_1_1_vector2_d_html_aecad9e083d41f03929fb01e60851dfa8"><div class="ttname"><a href="class_c_m_u462_1_1_vector2_d.html#aecad9e083d41f03929fb01e60851dfa8">CMU462::Vector2D::unit</a></div><div class="ttdeci">Vector2D unit(void) const </div><div class="ttdoc">Returns unit vector parallel to this one. </div><div class="ttdef"><b>Definition:</b> vector2D.h:112</div></div>
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