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</script></head><body><div id="package-header"><ul class="links" id="page-menu"><li><a href="src/Data-AffineSpace-Point.html">Source</a></li><li><a href="index.html">Contents</a></li><li><a href="doc-index.html">Index</a></li></ul><p class="caption">vector-space-points-0.2.1.1: A type for points, as distinct from vectors.</p></div><div id="content"><div id="module-header"><table class="info"><tr><th>Copyright</th><td>(c) 2011 Brent Yorgey</td></tr><tr><th>License</th><td>BSD-style (see LICENSE)</td></tr><tr><th>Maintainer</th><td>byorgey@cis.upenn.edu</td></tr><tr><th>Safe Haskell</th><td>None</td></tr><tr><th>Language</th><td>Haskell2010</td></tr></table><p class="caption">Data.AffineSpace.Point</p></div><div id="table-of-contents"><p class="caption">Contents</p><ul><li><a href="#g:1">Points</a></li><li><a href="#g:2">Reflection through a point</a></li></ul></div><div id="description"><p class="caption">Description</p><div class="doc"><p>A type for <em>points</em> (as distinct from vectors), with an appropriate
AffineSpace instance.</p></div></div><div id="synopsis"><p id="control.syn" class="caption expander" onclick="toggleSection('syn')">Synopsis</p><ul id="section.syn" class="hide" onclick="toggleSection('syn')"><li class="src short"><span class="keyword">newtype</span> <a href="#t:Point">Point</a> v = <a href="#v:P">P</a> v</li><li class="src short"><a href="#v:unPoint">unPoint</a> :: <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v -> v</li><li class="src short"><a href="#v:origin">origin</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AdditiveGroup.html#t:AdditiveGroup">AdditiveGroup</a> v => <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v</li><li class="src short"><a href="#v:-42-.">(*.)</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-VectorSpace.html#t:VectorSpace">VectorSpace</a> v => <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-VectorSpace.html#t:Scalar">Scalar</a> v -> <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v -> <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v</li><li class="src short"><a href="#v:mirror">mirror</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AdditiveGroup.html#t:AdditiveGroup">AdditiveGroup</a> v => <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v -> <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v</li><li class="src short"><a href="#v:relative">relative</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a> p => p -> (<a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p) -> p -> p</li><li class="src short"><a href="#v:relative2">relative2</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a> p => p -> (<a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p) -> p -> p -> p</li><li class="src short"><a href="#v:relative3">relative3</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a> p => p -> (<a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p) -> p -> p -> p -> p</li><li class="src short"><a href="#v:reflectThrough">reflectThrough</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a> p => p -> p -> p</li></ul></div><div id="interface"><h1 id="g:1">Points</h1><div class="top"><p class="src"><span class="keyword">newtype</span> <a name="t:Point" class="def">Point</a> v <a href="src/Data-AffineSpace-Point.html#Point" class="link">Source</a></p><div class="doc"><p><code>Point</code> is a newtype wrapper around vectors used to represent
points, so we don't get them mixed up. The distinction between
vectors and points is important: translations affect points, but
leave vectors unchanged. Points are instances of the
<code><a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a></code> class from <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html">Data.AffineSpace</a>.</p></div><div class="subs constructors"><p class="caption">Constructors</p><table><tr><td class="src"><a name="v:P" class="def">P</a> v</td><td class="doc empty"> </td></tr></table></div><div class="subs instances"><p id="control.i:Point" class="caption collapser" onclick="toggleSection('i:Point')">Instances</p><div id="section.i:Point" class="show"><table><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Functor.html#t:Functor">Functor</a> <a href="Data-AffineSpace-Point.html#t:Point">Point</a></span> <a href="src/Data-AffineSpace-Point.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> v => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Eq.html#t:Eq">Eq</a> (<a href="Data-AffineSpace-Point.html#t:Point">Point</a> v)</span> <a href="src/Data-AffineSpace-Point.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Data.html#t:Data">Data</a> v => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Data.html#t:Data">Data</a> (<a href="Data-AffineSpace-Point.html#t:Point">Point</a> v)</span> <a href="src/Data-AffineSpace-Point.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> v => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Data-Ord.html#t:Ord">Ord</a> (<a href="Data-AffineSpace-Point.html#t:Point">Point</a> v)</span> <a href="src/Data-AffineSpace-Point.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Read.html#t:Read">Read</a> v => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Read.html#t:Read">Read</a> (<a href="Data-AffineSpace-Point.html#t:Point">Point</a> v)</span> <a href="src/Data-AffineSpace-Point.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> v => <a href="file:///usr/share/doc/ghc-doc/html/libraries/base-4.8.2.0/Text-Show.html#t:Show">Show</a> (<a href="Data-AffineSpace-Point.html#t:Point">Point</a> v)</span> <a href="src/Data-AffineSpace-Point.html#line-43" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AdditiveGroup.html#t:AdditiveGroup">AdditiveGroup</a> v => <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a> (<a href="Data-AffineSpace-Point.html#t:Point">Point</a> v)</span> <a href="src/Data-AffineSpace-Point.html#line-57" class="link">Source</a></td><td class="doc empty"> </td></tr><tr><td class="src clearfix"><span class="inst-left"><span class="keyword">type</span> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> (<a href="Data-AffineSpace-Point.html#t:Point">Point</a> v) = v</span> <a href="src/Data-AffineSpace-Point.html#line-58" class="link">Source</a></td><td class="doc empty"> </td></tr></table></div></div></div><div class="top"><p class="src"><a name="v:unPoint" class="def">unPoint</a> :: <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v -> v <a href="src/Data-AffineSpace-Point.html#unPoint" class="link">Source</a></p><div class="doc"><p>Convert a point <code>p</code> into the vector from the origin to <code>p</code>. This
should be considered a "semantically unsafe" operation; think
carefully about whether and why you need to use it. The
recommended way to do this conversion would be to write <code>(p
<code><a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#v:.-45-.">.-.</a></code> <code><a href="Data-AffineSpace-Point.html#v:origin">origin</a></code>)</code>.</p></div></div><div class="top"><p class="src"><a name="v:origin" class="def">origin</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AdditiveGroup.html#t:AdditiveGroup">AdditiveGroup</a> v => <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v <a href="src/Data-AffineSpace-Point.html#origin" class="link">Source</a></p><div class="doc"><p>The origin of the vector space <code>v</code>.</p></div></div><div class="top"><p class="src"><a name="v:-42-." class="def">(*.)</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-VectorSpace.html#t:VectorSpace">VectorSpace</a> v => <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-VectorSpace.html#t:Scalar">Scalar</a> v -> <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v -> <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v <a href="src/Data-AffineSpace-Point.html#%2A." class="link">Source</a></p><div class="doc"><p>Scale a point by a scalar.</p></div></div><div class="top"><p class="src"><a name="v:mirror" class="def">mirror</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AdditiveGroup.html#t:AdditiveGroup">AdditiveGroup</a> v => <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v -> <a href="Data-AffineSpace-Point.html#t:Point">Point</a> v <a href="src/Data-AffineSpace-Point.html#mirror" class="link">Source</a></p><div class="doc"><p>Reflect a point through the <code><a href="Data-AffineSpace-Point.html#v:origin">origin</a></code>.</p></div></div><h1 id="g:2">Reflection through a point</h1><div class="top"><p class="src"><a name="v:relative" class="def">relative</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a> p => p -> (<a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p) -> p -> p <a href="src/Data-AffineSpace-Point.html#relative" class="link">Source</a></p><div class="doc"><p>Apply a transformation relative to the given point.</p></div></div><div class="top"><p class="src"><a name="v:relative2" class="def">relative2</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a> p => p -> (<a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p) -> p -> p -> p <a href="src/Data-AffineSpace-Point.html#relative2" class="link">Source</a></p><div class="doc"><p>Apply a transformation relative to the given point.</p></div></div><div class="top"><p class="src"><a name="v:relative3" class="def">relative3</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a> p => p -> (<a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p -> <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:Diff">Diff</a> p) -> p -> p -> p -> p <a href="src/Data-AffineSpace-Point.html#relative3" class="link">Source</a></p><div class="doc"><p>Apply a transformation relative to the given point.</p></div></div><div class="top"><p class="src"><a name="v:reflectThrough" class="def">reflectThrough</a> :: <a href="file:///usr/share/doc/libghc-vector-space-doc/html/Data-AffineSpace.html#t:AffineSpace">AffineSpace</a> p => p -> p -> p <a href="src/Data-AffineSpace-Point.html#reflectThrough" class="link">Source</a></p><div class="doc"><p>Mirror a point through a given point.</p></div></div></div></div><div id="footer"><p>Produced by <a href="http://www.haskell.org/haddock/">Haddock</a> version 2.16.1</p></div></body></html>
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