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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"  
  "http://www.w3.org/TR/html4/loose.dtd">  
<html > 
<head><title>nip2 for nerds</title> 
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"> 
<meta name="generator" content="TeX4ht (http://www.tug.org/tex4ht/)"> 
<meta name="originator" content="TeX4ht (http://www.tug.org/tex4ht/)"> 
<!-- 3,html --> 
<meta name="src" content="nipguide.tex"> 
<link rel="stylesheet" type="text/css" href="nipguide.css"> 
</head><body 
>
  <!--l. 317--><div class="crosslinks"><p class="noindent">[<a 
href="nipguidese2.html" >prev</a>] [<a 
href="nipguidese2.html#tailnipguidese2.html" >prev-tail</a>] [<a 
href="#tailnipguidese3.html">tail</a>] [<a 
href="nipguidech2.html#nipguidese3.html" >up</a>] </p></div>
  <h3 class="sectionHead"><span class="titlemark">2.3    </span> <a 
 id="x9-80002.3"></a><span 
class="phvr7t-x-x-80">nip2 </span>for nerds</h3>
<!--l. 318--><p class="noindent" ><a name="nip_label_sec:nerdtour"></a>
<!--l. 320--><p class="indent" >  This section sprints through a bit of <span 
class="phvr7t-x-x-80">nip2 </span>programming,
see <span 
class="cmsy-10"></span><a 
href="nipguidech6.html#x31-570006">6<!--tex4ht:ref: sec:program --></a> for full details and a more formal definition of the
language.
<!--l. 324--><p class="indent" >  The insides of <span 
class="phvr7t-x-x-80">nip2 </span>are built with <span 
class="phvr7t-x-x-80">nip2</span>&#8217;s own programming
language. It&#8217;s a pure lazy functional language with classes.
It&#8217;s C&#8217;s expression syntax (more or less) plus approximately
Miranda/Haskell function syntax, plus some basic class
stuff. <span 
class="phvr7t-x-x-80">nip2</span>&#8217;s main window is a class browser for this
programming language.
<!--l. 330--><p class="indent" >  Click on <span 
class="phvr7t-x-x-80">Toolkits </span>/ <span 
class="phvr7t-x-x-80">Edit Toolkits </span>in <span 
class="phvr7t-x-x-80">nip2</span>&#8217;s main window to
pop up the programming window (see <span 
class="cmsy-10"></span><a 
href="nipguidese12.html#x20-380004.4">4.4<!--tex4ht:ref: sec:progwin --></a> for details on
all the bits in the window), then in the edit area there
type:
                                                 <div class="verbatim" id="verbatim-1">
  //&#x00A0;add&#x00A0;two&#x00A0;things
 &#x00A0;<br />
 &#x00A0;<br />Fred&#x00A0;a&#x00A0;b&#x00A0;=&#x00A0;class&#x00A0;{
 &#x00A0;<br />&#x00A0;&#x00A0;sum&#x00A0;=&#x00A0;a&#x00A0;+&#x00A0;b;
 &#x00A0;<br />} 
</div>
<!--l. 340--><p class="nopar" >
<!--l. 342--><p class="indent" >  This defines a class called <span 
class="phvr7t-x-x-80">Fred </span>whose constructor takes
two arguments, <span 
class="phvr7t-x-x-80">a </span>and <span 
class="phvr7t-x-x-80">b</span>. There&#8217;s one member, called <span 
class="phvr7t-x-x-80">sum</span>,
which is <span 
class="phvr7t-x-x-80">a </span>and <span 
class="phvr7t-x-x-80">b </span>added together.
<!--l. 346--><p class="indent" >    In the program window, click <span 
class="phvr7t-x-x-80">File </span>/ <span 
class="phvr7t-x-x-80">Process</span>. This
makes <span 
class="phvr7t-x-x-80">nip2 </span>read what you typed, parse it, compile it and
update itself. The program window should now look like
Figure&#x00A0;<a 
href="#x9-800111">2.11<!--tex4ht:ref: fg:Fred --></a>.
<!--l. 350--><p class="indent" >    <hr class="figure"><div class="figure" 
>
                                                                                       

                                                                                       
<a 
 id="x9-800111"></a>
                                           
                                                                                       

                                                                                       
<div class="center" 
>
<!--l. 351--><p class="noindent" >
<!--l. 351--><p class="noindent" ><img 
src="figs/snap8.jpg" alt="PIC"  
></div>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;2.11: </span><span  
class="content">Programming <span 
class="phvr7t-x-x-80">Fred</span></span></div><!--tex4ht:label?: x9-800111 -->
<!--l. 353--><p class="noindent" ><a name="nip_label_fg:Fred"></a>
                                           
                                                                                       

                                                                                       
<!--l. 354--><p class="indent" >  </div><hr class="endfigure">
<!--l. 356--><p class="indent" >  If you look back at the main <span 
class="phvr7t-x-x-80">nip2 </span>window, a new
menu will have appeared under <span 
class="phvr7t-x-x-80">Toolkits </span>called <span 
class="phvr7t-x-x-80">untitled</span>.
If you click on that, there will be a menu item called
<span 
class="phvr7t-x-x-80">Fred</span>. Let your mouse linger, and you&#8217;ll see a tooltip
too.
<!--l. 361--><p class="indent" >  In the main window, type <span 
class="phvr7t-x-x-80">Fred 2 3 </span>into the box at the
bottom of the current column. Press Return and <span 
class="phvr7t-x-x-80">nip2</span>
will make a <span 
class="phvr7t-x-x-80">Fred </span>for you. Click on the down arrow to
the left of your new <span 
class="phvr7t-x-x-80">Fred </span>once to see the members of
<span 
class="phvr7t-x-x-80">Fred </span>(just <span 
class="phvr7t-x-x-80">sum </span>in this case), click again to see the class
parameters too. The main window should look like
Figure&#x00A0;<a 
href="#x9-800212">2.12<!--tex4ht:ref: fg:mainFred --></a>.
<!--l. 367--><p class="indent" >  <hr class="figure"><div class="figure" 
>
                                           
                                                                                       

                                                                                       
<a 
 id="x9-800212"></a>
                                           
                                                                                       

                                                                                       
<div class="center" 
>
<!--l. 368--><p class="noindent" >
<!--l. 368--><p class="noindent" ><img 
src="figs/snap9.jpg" alt="PIC"  
></div>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;2.12: </span><span  
class="content">Main window <span 
class="phvr7t-x-x-80">Fred</span></span></div><!--tex4ht:label?: x9-800212 -->
<!--l. 370--><p class="noindent" ><a name="nip_label_fg:mainFred"></a>
                                           
                                                                                       

                                                                                       
<!--l. 371--><p class="indent" >  </div><hr class="endfigure">
<!--l. 373--><p class="indent" >  Click to the right of <span 
class="phvr7t-x-x-80">b</span>, type in a new value and press
Return. The <span 
class="phvr7t-x-x-80">sum </span>member should update. <span 
class="phvr7t-x-x-80">nip2 </span>keeps track of
dependencies between rows, but it also tracks dependencies
inside rows, both ones that come from the class, and ones
created by any edits you do to the class instance after
creating it. You won&#8217;t see it in a simple example, but <span 
class="phvr7t-x-x-80">nip2</span>
also discovers and tracks dependencies which can arise at
run time. Click on the text just to the right of the <span 
class="phvr7t-x-x-80">b </span>button
again, type <span 
class="phvr7t-x-x-80">a </span>and press Return. Now edit <span 
class="phvr7t-x-x-80">a</span>: press Return and
both <span 
class="phvr7t-x-x-80">b </span>and <span 
class="phvr7t-x-x-80">sum </span>will update.
<!--l. 383--><p class="indent" >  You can use <span 
class="phvr7t-x-x-80">Fred </span>to add any two things together.
Click on <span 
class="phvr7t-x-x-80">Toolkits </span>/ <span 
class="phvr7t-x-x-80">Widgets </span>/ <span 
class="phvr7t-x-x-80">Scale </span>to make a scale widget,
press Ctrl-U (the keyboard shortcut for <span 
class="phvr7t-x-x-80">Edit </span>/ <span 
class="phvr7t-x-x-80">Duplicate</span>)
to duplicate it, and finally click on <span 
class="phvr7t-x-x-80">Toolkits </span>/ <span 
class="phvr7t-x-x-80">untitled </span>/
<span 
class="phvr7t-x-x-80">Fred</span>. Open up the new <span 
class="phvr7t-x-x-80">Fred </span>and try dragging some of
the scales around. The main window will look like
Figure&#x00A0;<a 
href="#x9-800313">2.13<!--tex4ht:ref: fg:slideFred --></a>.
<!--l. 390--><p class="indent" >  <hr class="figure"><div class="figure" 
>
                                           
                                                                                       

                                                                                       
<a 
 id="x9-800313"></a>
                                           
                                                                                       

                                                                                       
<div class="center" 
>
<!--l. 391--><p class="noindent" >
<!--l. 391--><p class="noindent" ><img 
src="figs/snap10.jpg" alt="PIC"  
></div>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;2.13: </span><span  
class="content">Scale <span 
class="phvr7t-x-x-80">Fred</span></span></div><!--tex4ht:label?: x9-800313 -->
<!--l. 393--><p class="noindent" ><a name="nip_label_fg:slideFred"></a>
                                           
                                                                                       

                                                                                       
<!--l. 394--><p class="indent" >  </div><hr class="endfigure">
<!--l. 396--><p class="indent" >  The scales are classes too (instances of <span 
class="phvr7t-x-x-80">Scale</span>). You can
open them up and do strange things with them as well. Open
up one of the scales you made (eg. <span 
class="phvr7t-x-x-80">A2 </span>in Figure&#x00A0;<a 
href="#x9-800313">2.13<!--tex4ht:ref: fg:slideFred --></a>) and
change the <span 
class="phvr7t-x-x-80">from </span>parameter to be <span 
class="phvr7t-x-x-80">A3.value</span>. Now try dragging
the sliders again.
<!--l. 401--><p class="indent" >  Try dragging the <span 
class="phvr7t-x-x-80">sum </span>slider. Now go back and drag one of
the original sliders. You&#8217;ll see that <span 
class="phvr7t-x-x-80">sum </span>no longer updates,
it&#8217;s stuck at the last position you dragged it to. This is
because there are now two things affecting the value of <span 
class="phvr7t-x-x-80">sum</span>:
the underlying code (the <span 
class="phvr7t-x-x-80">a + b </span>inside <span 
class="phvr7t-x-x-80">Fred</span>), and the position
you dragged the slider representing <span 
class="phvr7t-x-x-80">sum </span>to. <span 
class="phvr7t-x-x-80">nip2 </span>has the rule
that graphical edits (dragging the slider) override code. To
make <span 
class="phvr7t-x-x-80">sum </span>update again, right click on the <span 
class="phvr7t-x-x-80">sum </span>button and
select <span 
class="phvr7t-x-x-80">Reset </span>from the pop up menu. Now drag one of the
input sliders again, and <span 
class="phvr7t-x-x-80">sum </span>will start updating once
more.
<!--l. 411--><p class="indent" >  Classes can inherit from other classes. Go back to the
program window, click on <span 
class="phvr7t-x-x-80">File </span>/ <span 
class="phvr7t-x-x-80">New </span>/ <span 
class="phvr7t-x-x-80">Tool </span>to clear the edit
window, and type:
                                                 <div class="verbatim" id="verbatim-2">
  //&#x00A0;multiply&#x00A0;two&#x00A0;things
 &#x00A0;<br />
 &#x00A0;<br />Jim&#x00A0;a&#x00A0;b&#x00A0;=&#x00A0;class&#x00A0;Fred&#x00A0;a&#x00A0;b&#x00A0;{
 &#x00A0;<br />&#x00A0;&#x00A0;product&#x00A0;=&#x00A0;a&#x00A0;&#x22C6;&#x00A0;b;
 &#x00A0;<br />} 
</div>
<!--l. 420--><p class="nopar" >
<!--l. 422--><p class="indent" >  This defines a class called <span 
class="phvr7t-x-x-80">Jim </span>which inherits from <span 
class="phvr7t-x-x-80">Fred</span>.
Click <span 
class="phvr7t-x-x-80">File </span>/ <span 
class="phvr7t-x-x-80">Process</span>, then back in the main window, type <span 
class="phvr7t-x-x-80">Jim 4</span>
<span 
class="phvr7t-x-x-80">5 </span>into the bottom of the column. Click down once to expose
the members (just <span 
class="phvr7t-x-x-80">product</span>), click again to expose the
parameters as well (<span 
class="phvr7t-x-x-80">a </span>and <span 
class="phvr7t-x-x-80">b</span>), and click a third time
to expose the superclass member (which should be
an instance of <span 
class="phvr7t-x-x-80">Fred</span>). You can also open up the <span 
class="phvr7t-x-x-80">super</span>
member and see inside the <span 
class="phvr7t-x-x-80">Fred </span>that this <span 
class="phvr7t-x-x-80">Jim </span>is using as its
superclass. <span 
class="phvr7t-x-x-80">A5 </span>will respond to both <span 
class="phvr7t-x-x-80">product </span>and <span 
class="phvr7t-x-x-80">sum</span>. See
Figure&#x00A0;<a 
href="#x9-800414">2.14<!--tex4ht:ref: fg:Jim --></a>.
<!--l. 433--><p class="indent" >    <hr class="figure"><div class="figure" 
>
                                                                                       

                                                                                       
<a 
 id="x9-800414"></a>
                                           
                                                                                       

                                                                                       
<div class="center" 
>
<!--l. 434--><p class="noindent" >
<!--l. 434--><p class="noindent" ><img 
src="figs/snap11.jpg" alt="PIC"  
></div>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;2.14: </span><span  
class="content">Browsing <span 
class="phvr7t-x-x-80">Jim</span></span></div><!--tex4ht:label?: x9-800414 -->
<!--l. 436--><p class="noindent" ><a name="nip_label_fg:Jim"></a>
                                           
                                                                                       

                                                                                       
<!--l. 437--><p class="indent" >  </div><hr class="endfigure">
<!--l. 439--><p class="indent" >  <span 
class="phvr7t-x-x-80">nip2 </span>has about 20 different graphical classes like
<span 
class="phvr7t-x-x-80">Scale</span>. Whenever a row takes a new value, <span 
class="phvr7t-x-x-80">nip2 </span>checks to
see if that value is an instance of one of these special
classes, and if it is, it will add a graphical element to
the row display which represents that class&#8217;s value. It
builds the graphical part by looking inside the class
for certain members (for example, the scale graphic
looks for members called <span 
class="phvr7t-x-x-80">from</span>, <span 
class="phvr7t-x-x-80">to </span>and <span 
class="phvr7t-x-x-80">value</span>). When you
change the graphic (maybe by dragging the scale), <span 
class="phvr7t-x-x-80">nip2</span>
rebuilds the class by looking inside for a edit member (eg.
<span 
class="phvr7t-x-x-80">Scale</span><span 
class="phvr7t-x-x-80">_edit</span>) or if that&#8217;s not defined, a constructor member (eg.
<span 
class="phvr7t-x-x-80">Scale</span>).
<!--l. 449--><p class="indent" >  You can make your own graphic widgets by subclassing
<span 
class="phvr7t-x-x-80">nip2</span>&#8217;s built-in ones. By selectively overriding default
constructors and adding edit members, you can control how
your new widget will behave in expressions, and how it will
behave if it&#8217;s edited graphically.
<!--l. 454--><p class="indent" >  Make a new column, load up an image (use <span 
class="phvr7t-x-x-80">File </span>/ <span 
class="phvr7t-x-x-80">Open</span>),
open an image viewer (double-click on the thumbnail), drag
out two regions on it (hold down Ctrl and the left mouse
button and drag down and right). Your main window should
look like Figure&#x00A0;<a 
href="#x9-800515">2.15<!--tex4ht:ref: fg:twomoreregions --></a>.
<!--l. 459--><p class="indent" >  <hr class="figure"><div class="figure" 
>
                                           
                                                                                       

                                                                                       
<a 
 id="x9-800515"></a>
                                           
                                                                                       

                                                                                       
<div class="center" 
>
<!--l. 460--><p class="noindent" >
<!--l. 460--><p class="noindent" ><img 
src="figs/snap12.jpg" alt="PIC"  
></div>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;2.15: </span><span  
class="content">Two more regions</span></div><!--tex4ht:label?: x9-800515 -->
<!--l. 462--><p class="noindent" ><a name="nip_label_fg:twomoreregions"></a>
                                           
                                                                                       

                                                                                       
<!--l. 463--><p class="indent" >  </div><hr class="endfigure">
<!--l. 465--><p class="indent" >  <span 
class="phvr7t-x-x-80">im</span><span 
class="phvr7t-x-x-80">_insert </span>is a VIPS operation that puts one image inside
another at an (x, y) position. VIPS operations work on VIPS
images. The <span 
class="phvr7t-x-x-80">value </span>member of an <span 
class="phvr7t-x-x-80">Image </span>or <span 
class="phvr7t-x-x-80">Region </span>is the VIPS
image that underlies the <span 
class="phvr7t-x-x-80">nip2 </span>row.
<!--l. 469--><p class="indent" >  You can use <span 
class="phvr7t-x-x-80">im</span><span 
class="phvr7t-x-x-80">_insert </span>to make a thing to join two images
together. Back in the program window, click on <span 
class="phvr7t-x-x-80">File </span>/ <span 
class="phvr7t-x-x-80">New </span>/
<span 
class="phvr7t-x-x-80">Tool </span>and enter:
                                                 <div class="verbatim" id="verbatim-3">
  //&#x00A0;join&#x00A0;two&#x00A0;images&#x00A0;left-right
 &#x00A0;<br />
 &#x00A0;<br />Join&#x00A0;a&#x00A0;b&#x00A0;=&#x00A0;class&#x00A0;Image&#x00A0;value&#x00A0;{
 &#x00A0;<br />&#x00A0;&#x00A0;shim&#x00A0;=&#x00A0;Scale&#x00A0;"Spacing"&#x00A0;0&#x00A0;1000&#x00A0;0;
 &#x00A0;<br />&#x00A0;&#x00A0;value&#x00A0;=&#x00A0;im_insert&#x00A0;a.value&#x00A0;b.value
 &#x00A0;<br />&#x00A0;&#x00A0;&#x00A0;&#x00A0;(a.width&#x00A0;+&#x00A0;shim.value)&#x00A0;0;
 &#x00A0;<br />} 
</div>
<!--l. 480--><p class="nopar" >
<!--l. 482--><p class="noindent" >Click <span 
class="phvr7t-x-x-80">File </span>/ <span 
class="phvr7t-x-x-80">Process</span>. This defines a class <span 
class="phvr7t-x-x-80">Join </span>which subclasses
the <span 
class="phvr7t-x-x-80">Image </span>graphic.
<!--l. 486--><p class="indent" >    Now select your two regions (click on the first one,
shift-click on the second) and click on <span 
class="phvr7t-x-x-80">Toolkits </span>/ <span 
class="phvr7t-x-x-80">untitled </span>/ <span 
class="phvr7t-x-x-80">Join</span>.
Alternatively, just click <span 
class="phvr7t-x-x-80">Join </span>and it&#8217;ll be given the borrom
two items in the column. A new <span 
class="phvr7t-x-x-80">Join </span>row will appear. Open
it up and drag the slider to set the spacing between the two
joined images. Go back to the image viewer for the image
file you loaded and try dragging one of the regions.
Figure&#x00A0;<a 
href="#x9-800616">2.16<!--tex4ht:ref: fg:myjoin --></a> shows this class in action. The thing in <span 
class="phvr7t-x-x-80">Toolkits </span>/
<span 
class="phvr7t-x-x-80">Image </span>/ <span 
class="phvr7t-x-x-80">Join </span>/ <span 
class="phvr7t-x-x-80">Left to Right </span>is just a slightly fancier version of
this.
<!--l. 497--><p class="indent" >    <hr class="figure"><div class="figure" 
>
                                                                                       

                                                                                       
<a 
 id="x9-800616"></a>
                                           
                                                                                       

                                                                                       
<div class="center" 
>
<!--l. 498--><p class="noindent" >
<!--l. 498--><p class="noindent" ><img 
src="figs/snap13.jpg" alt="PIC"  
></div>
<br /> <div class="caption" 
><span class="id">Figure&#x00A0;2.16: </span><span  
class="content">Joining two images with <span 
class="phvr7t-x-x-80">Join</span></span></div><!--tex4ht:label?: x9-800616 -->
<!--l. 500--><p class="noindent" ><a name="nip_label_fg:myjoin"></a>
                                           
                                                                                       

                                                                                       
<!--l. 501--><p class="indent" >  </div><hr class="endfigure">
<!--l. 503--><p class="indent" >  You can change how the graphic widgets behave by
subclassing them. Try:
                                                 <div class="verbatim" id="verbatim-4">
  Scale_int&#x00A0;c&#x00A0;f&#x00A0;t&#x00A0;v&#x00A0;=&#x00A0;class
 &#x00A0;<br />&#x00A0;&#x00A0;scope.Scale&#x00A0;c&#x00A0;f&#x00A0;t&#x00A0;((int)&#x00A0;v)&#x00A0;{
 &#x00A0;<br />&#x00A0;&#x00A0;Scale&#x00A0;=&#x00A0;Scale_int;
 &#x00A0;<br />} 
</div>
<!--l. 510--><p class="nopar" >
<!--l. 512--><p class="noindent" >This defines a new scale class called <span 
class="phvr7t-x-x-80">Scale</span><span 
class="phvr7t-x-x-80">_int </span>which can
only take integer values. The <span 
class="phvr7t-x-x-80">Scale = Scale</span><span 
class="phvr7t-x-x-80">_int; </span>line is
<span 
class="phvr7t-x-x-80">Scale</span><span 
class="phvr7t-x-x-80">_int </span>overriding <span 
class="phvr7t-x-x-80">Scale</span>&#8217;s constructor, so that a <span 
class="phvr7t-x-x-80">Scale</span><span 
class="phvr7t-x-x-80">_int</span>
stays a <span 
class="phvr7t-x-x-80">Scale</span><span 
class="phvr7t-x-x-80">_int </span>when you drag. Because there&#8217;s a local
called <span 
class="phvr7t-x-x-80">Scale</span>, <span 
class="phvr7t-x-x-80">Scale</span><span 
class="phvr7t-x-x-80">_int </span>needs to use <span 
class="phvr7t-x-x-80">scope.Scale </span>to refer to the
superclass.
<!--l. 519--><p class="indent" >    Here&#8217;s a version of <span 
class="phvr7t-x-x-80">Mark </span>which can only be dragged in a
circle. You pass it an image to display on, an xy centre
position, a radius and a start angle.
                                                                                       

                                                                                       
  <div class="verbatim" id="verbatim-5">
Mark_circle&#x00A0;image&#x00A0;x&#x00A0;y&#x00A0;r&#x00A0;a&#x00A0;=&#x00A0;class
&#x00A0;<br />&#x00A0;&#x00A0;scope.Mark&#x00A0;image&#x00A0;_x'&#x00A0;_y'&#x00A0;{
&#x00A0;<br />&#x00A0;&#x00A0;//&#x00A0;get&#x00A0;rect&#x00A0;cods&#x00A0;for&#x00A0;our&#x00A0;point
&#x00A0;<br />&#x00A0;&#x00A0;_pos&#x00A0;=&#x00A0;(x,&#x00A0;y)&#x00A0;+&#x00A0;rectangular&#x00A0;(r,&#x00A0;a);
&#x00A0;<br />&#x00A0;&#x00A0;_x'&#x00A0;=&#x00A0;re&#x00A0;_pos;
&#x00A0;<br />&#x00A0;&#x00A0;_y'&#x00A0;=&#x00A0;im&#x00A0;_pos;
&#x00A0;<br />
&#x00A0;<br />&#x00A0;&#x00A0;Mark&#x00A0;i&#x00A0;l&#x00A0;t
&#x00A0;<br />&#x00A0;&#x00A0;&#x00A0;&#x00A0;=&#x00A0;this.Mark_circle&#x00A0;i&#x00A0;x&#x00A0;y&#x00A0;r&#x00A0;a'
&#x00A0;<br />&#x00A0;&#x00A0;{
&#x00A0;<br />&#x00A0;&#x00A0;&#x00A0;&#x00A0;//&#x00A0;vector&#x00A0;from&#x00A0;centre&#x00A0;of
&#x00A0;<br />&#x00A0;&#x00A0;&#x00A0;&#x00A0;//&#x00A0;circle&#x00A0;to&#x00A0;new&#x00A0;position
&#x00A0;<br />&#x00A0;&#x00A0;&#x00A0;&#x00A0;u&#x00A0;=&#x00A0;(l,&#x00A0;t)&#x00A0;-&#x00A0;(x,&#x00A0;y);
&#x00A0;<br />
&#x00A0;<br />&#x00A0;&#x00A0;&#x00A0;&#x00A0;//&#x00A0;angle&#x00A0;of&#x00A0;vector
&#x00A0;<br />&#x00A0;&#x00A0;&#x00A0;&#x00A0;a'&#x00A0;=&#x00A0;im&#x00A0;(polar&#x00A0;u);
&#x00A0;<br />&#x00A0;&#x00A0;}
&#x00A0;<br />}
</div>
<!--l. 541--><p class="nopar" >
                                           
                                                                                       

                                                                                       
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