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<DIV>

  <H1 CLASS="Title" align="center"> <font color="#FF0000">Simple 3D Programming 

    Using VPython</font> </H1>

<DIV>

    <H3 CLASS="Heading-1"> <font color="#0000A0">I. VPython: the Python/ Visual / 

      IDLE environment</font></H3>

<P CLASS="Normal">

The interactive development environment you will use is called &quot;IDLE.&quot;</P>

</DIV>

<DIV>

    <H3 CLASS="Heading2"> <font color="#0000A0">The Display window</font></H3>

<P CLASS="Normal">

When using VPython the display window shows objects in 3D.</P>

<P CLASS="Normal">

(0,0,0) is in the center of the display window<IMG SRC="axes.gif" ALIGN="RIGHT">

. The +x axis runs to the right, the +y axis runs up, and the +z axis points out of the screen, toward you.</P>

    <P CLASS="Normal"> x, y, and z are measured in whatever units you choose; 

      the display is automatically scaled appropriately. (You could, for example, 

      create a sphere with a radius of 1E-15 m to represent a nucleus, or a sphere 

      with a radius of 1E6 m to represent a planet, though it wouldn't make sense 

      to put both of these objects in the same display!)</P>

</DIV>

<DIV>

    <H3 CLASS="Heading2"> <font color="#0000A0">The Output window</font></H3>

<P CLASS="Normal">

The output of any -print- statements you execute in your program goes to the Output window, which is a scrolling text window. You can use this window to print values of variables, print lists, print messages, etc. Place it where you can see messages in it.</P>

</DIV>

<DIV>

    <H3 CLASS="Heading2"> <font color="#0000A0">The Code window</font></H3>

    <P CLASS="Normal"> If you type the following simple program into the code 
      window in IDLE and run it (press F5, or use the Run menu), you will see 
      a display like the one shown in the figure below. </P>

    <P CLASS="program"> from visual import *</P>

    <P CLASS="program"> redbox=box(pos=vector(4,2,3), size=(8.,4.,6.),color=color.red)</P>

<P CLASS="program">

greenball=sphere(pos=vector(4,7,3), radius=2, color=color.green)</P>

    <P CLASS="Normal"> Visual is the name of the 3D graphics module used with 

      the Python programming language. VPython is the name of the combination 

      of the Python programming language, the Visual module, and the development 

      environment IDLE.</P>

    <h3 class="Heading2"><font color="#0000A0">Viewing the scene</font></h3>

    <p class="Normal"> In the display window, click and drag with the right mouse 
      button (hold down the shift key on a Macintosh). Drag left or right, and 
      you rotate around the scene. To rotate around a horizontal axis, drag up 
      or down with the right mouse button. Click and drag up or down with the 
      middle mouse button to move closer to the scene or farther away (on a 2-button 
      mouse, hold down the left and right buttons; on a 1-button mouse, hold down 
      the CTRL key).</p>

    <div></div>

    <div></div>

  </DIV>

<DIV>

    <H3 CLASS="Heading-1"> <font color="#0000A0">II. Visual Entities</font><IMG SRC="spherebox.gif" ALIGN="RIGHT"> 

    </H3>

</DIV>

<DIV>

    <H3 CLASS="Heading2"> <font color="#0000A0">Objects, names, and attributes</font></H3>

    <P CLASS="Normal"> The graphical objects you create, such as spheres, boxes, 

      and curves, continue to exist for the duration of your program, and the 

      Visual 3D graphics module will continue to display them, wherever they are. 

      You must give each object a name (such as <span class="attribute">redbox</span> 

      or <span class="attribute">greenball</span> in the example above) if you 

      wish to refer to it again later in your program. All objects have attributes: 

      properties like <span class="attribute">greenball.pos</span> (the position 

      of the sphere), <span class="attribute">greenball.color</span>, and <span class="attribute">radius</span> 

      or other size parameter. If you change an attribute of an object, such as 

      its position or color, Visual will automatically display the object in its 

      new location, or with its new color.</P>

<P CLASS="Normal">

You can set the values of attributes in the &quot;constructor&quot; (the code used to create the object), and you can also modify attributes later:</P>

    <P CLASS="program"> greenball.radius = 2.2</P>

    <P CLASS="Normal"> In addition to the built-in set of attributes, you may 

      create new attributes. For example, you might create a sphere named <span class="attribute">moon</span>; 

      in addition to its radius and location, you might give it attributes such 

      as mass (<span class="attribute">moon.mass</span>) and momentum (<span class="attribute">moon.momentum</span>).</P>

    <h3 class="Heading2"><font color="#0000A0">Vectors</font></h3>

    <p class="Normal"> </p>

    <P CLASS="heading-4">Not all objects in Visual are visible objects. For example, 

      Visual allows you to create 3D vector quantities, and to perform vector 

      operations on them. If you create a vector quantity called <EM CLASS="code">a</EM>, 

      you may refer to its components as <EM CLASS="code">a.x</EM>, <EM CLASS="code"> 

      a.y</EM>, and <EM CLASS="code"> a.z</EM>. To add two vectors, <EM CLASS="code"> 

      a</EM> and <EM CLASS="code"> b</EM>, however, you do not need to add the 

      components one by one; Visual will do the vector addition for you:</P>

  </DIV>

  <DIV><P CLASS="program"> a = vector(1.,2.,3.)</P>

<P CLASS="program">

b = vector(4.,5.,6.)</P>

<P CLASS="program">

c=a+b</P>

    <P CLASS="Normal"> If you print <EM CLASS="code"> c</EM> , you will find that 

      it is a vector with components (5.,7.,9.).</P>

    <h3 class="Heading2"><font color="#0000A0">Scalar multiplication</font></h3>

    <p class="Normal"> </p>

    <p class="program"></p>

    <P CLASS="program">d = 3.*a # d is a vector with components (3., 6., 9.)</P>

    <DIV></DIV>

    <DIV> 

      <h3 class="Heading2"><font color="#0000A0">Vector magnitude</font></h3>

      <p class="Normal"> </p>

      <P CLASS="program">d = mag(c) # d is a scalar</P>

      <P CLASS="program"> z = mag(c)**2 # you can't square a vector; just its magnitude</P>

      

    </DIV>

    <DIV> 

      <h3 class="Heading2"><font color="#0000A0">Vector products</font></h3>

      <p class="Normal"> </p>

      <P CLASS="program">f = cross(a,b) # cross product</P>

<P CLASS="program">

g = dot(a,b)			# dot product</P>

      <P CLASS="program"> h = norm(a) # normalized (unit) vector</P>

      <P CLASS="Normal"> The attributes of Visual objects can be vectors, such 

        as velocity or momentum.</P>

    </DIV>

</DIV>

<DIV>

    <H3 CLASS="Heading-1"> <font color="#0000A0">III. Simple Python Programming</font></H3>

</DIV>

  <DIV> 

    <H3 CLASS="Heading2"><font color="#0000A0">Importing the 3D Graphics Module 

      (Visual)</font></H3>

    <div>

<p class="Normal"> The first line of your program must be:</p>

      <p class="program"> from visual import *</p>

    </div>

    <div> 

      <h3 class="Heading2"><font color="#0000A0"></font></h3>

    </div>

    <H3 CLASS="Heading2"><font color="#0000A0">Comments</font></H3>

<P CLASS="Normal">

A comment in a Python program starts with &quot;#&quot;</P>

    <P CLASS="program"> # this line is a comment</P>

    

  </DIV>

  <DIV>

    <H3 CLASS="Heading2"><font color="#0000A0">Variables</font></H3>

  </DIV>

  <DIV>

<P CLASS="Normal">

Variables can be created anywhere in a Python program, simply by assigning a variable name to a value. The type of the variable is determined by the assignment statement.</P>

    <P CLASS="program"> a = 3 #<span class="program"> an integer</span></P>

    <P CLASS="program"><span class="program"> b = -2. # a floating-point number</span></P>

    <P CLASS="program"><span class="program"> c = vector(0.4, 3e3, -1e1) # a vector 

      </span></P>

    <P CLASS="program"><span class="program"> Earth = sphere(pos=(0,0,0), radius=6.4e6) 

      # a Visual object</span></P>

    <P CLASS="program"><span class="program"> bodies = [ship, Ea</span>rth, Moon]	

      # a list of objects</P>

    <P CLASS="Normal"> Basic Visual objects such as sphere() and box() have a set 

      of attributes such as color, and you can define additional attributes such 

      as mass or momentum. Other objects, such as vector(), have built-in attributes 

      but you cannot create additional attributes. Numbers, lists, and other built-in 

      objects do not have attributes at all.</P>

    

  </DIV>

  <DIV>

<H3 CLASS="Heading2"><font color="#0000A0">Warning about division</font></H3>

<P CLASS="Normal">

Division of integers will not come out the way you may expect, since the result is rounded down to the nearest integer. Thus:</P>

    <P CLASS="program"> a = 2/3</P>

<P CLASS="program">

print a		# a is 0</P>

    <P CLASS="Normal"> To avoid this, place a decimal point after every number, like 
      this:</P>

    <P CLASS="program"> b = 2./3.</P>

    <P CLASS="program"> print b # b is 0.6666667, as expected</P>

  </DIV>

  <DIV> 
    <div> 
      <p class="Normal">We recommend putting the following statement at the start 
        of your program, in which case 2/3 will be 0.6666667; there are two underscores 
        before and after the word &quot;future&quot;:</p>
      <p class="program"> from __future__ import division</p>
      <h3 class="Heading2"><font color="#0000A0">Exponentiation</font></h3>
      <p> </p>
    </div>
    <P CLASS="program"> x**2 # Not x^2</P>

    <P CLASS="program">10**-2 gives an error; use 10.**-2</P>

  </DIV>

<DIV>

    <H3 CLASS="Heading2"> <font color="#0000A0">Logical Tests</font></H3>

    <P> If, elif (&quot;else if&quot;), else:</P>

    <P CLASS="program"> if a == b: # see table of logical expressions below</P>

    <P CLASS="program"> &nbsp;&nbsp;&nbsp;&nbsp;c = 3.5 # indented code executed 

      if test is true</P>

<P CLASS="program">

elif a &lt; b:</P>

    <P CLASS="program"> &nbsp;&nbsp;&nbsp;&nbsp;c = 0. # c will be set to zero 

      only if a &lt; b</P>

<P CLASS="program">

else:</P>

    <P CLASS="program"> &nbsp;&nbsp;&nbsp;&nbsp;c = -23.2</P>

    <P CLASS="program">&nbsp;</P>

</DIV>

<DIV>

    <H3 CLASS="Heading2"> <font color="#0000A0">Logical expressions</font></H3>

<TABLE BORDER="1">

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

==</P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

equal</P>

</TD>

</TR>

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

!=</P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

not equal (also &lt;&gt;)</P>

</TD>

</TR>

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

&lt;</P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

less than</P>

</TD>

</TR>

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

&gt; </P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

greater than</P>

</TD>

</TR>

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

&lt;=</P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

less than or equal </P>

</TD>

</TR>

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

&gt;=</P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

greater or equal</P>

</TD>

</TR>

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

or</P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

logical or</P>

</TD>

</TR>

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

and</P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

logical and</P>

</TD>

</TR>

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

in</P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

member of a sequence</P>

</TD>

</TR>

<TR>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

not in</P>

</TD>

<TD ROWSPAN="1" COLSPAN="1">

<P CLASS="program">

not sequence member</P>

</TD>

</TR>

</TABLE>

  </DIV>

<DIV>

    <H3 CLASS="Heading2">&nbsp; </H3>

    <H3 CLASS="Heading2"><font color="#0000A0">Lists</font></H3>

<P CLASS="Normal">

A list is an ordered sequence of any kind of object. It is delimited by square brackets.</P>

    <P CLASS="program"> moons = [Io, Europa, Ganymede, Callisto]</P>

    <P CLASS="Normal"> The function &quot;arange&quot; (short for &quot;arrayrange&quot;) 
      creates a sequence of numbers:</P>

    <P CLASS="program"> angles = arange (0., 2.*pi, pi/100.) </P>

<P CLASS="program">

# numbers from 0. to 2.*pi-(pi/100.) in steps of (pi/100.)</P>

<P CLASS="program">&nbsp;

</P>

    <P CLASS="program"> numbers = arange(10) # integer argument -&gt; integers</P>

    <P CLASS="program"> print numbers # [0,1,2,3,4,5,6,7,8,9] </P>

    <P CLASS="program">&nbsp; </P>

</DIV>

<DIV>

    <H3 CLASS="Heading2"> <font color="#0000A0">Loops</font></H3>

<P CLASS="Normal">

The simplest loop in Python is a &quot;while&quot; loop. The loop continues as long as the specified logical expression is true:</P>

    <P CLASS="program"> while x &lt; 23:</P>

    <P CLASS="program"> &nbsp;&nbsp;&nbsp;&nbsp;x = x + vx*dt</P>

<P CLASS="Normal">

To write an infinite loop, just use a logical expression that will always be true:</P>

    <P CLASS="program"> while 1==1:</P>

    <P CLASS="program"> &nbsp;&nbsp;&nbsp;&nbsp;ball.pos = ball.pos + (ball.momentum/ball.mass)*dt</P>

<P CLASS="Normal">

Since the value assigned to a true logical expression is 1, the following also produces an infinite loop:</P>

    <P CLASS="program"> while 1:</P>

    <P CLASS="program"> &nbsp;&nbsp;&nbsp;&nbsp;a = b+c</P>

<P CLASS="Normal">

Infinite loops are ok, because you can always interrupt the program by choosing &quot;Stop Program&quot; from the Run menu in IDLE.</P>

<P CLASS="Normal">

It is also possible to loop over the members of a sequence:</P>

    <P CLASS="program"> moons = [Io, Europa, Ganymede, Callisto]</P>

    <P CLASS="program"> for a in moons:</P>

    <P CLASS="program"> &nbsp;&nbsp;&nbsp;&nbsp;r = a.pos - Jupiter.pos</P>

    <P CLASS="program">&nbsp; </P>

    <P CLASS="program">for x in arange(10):</P>

<P CLASS="program">

	# see &quot;lists&quot; above</P>

<P CLASS="program">

	...</P>

    <P CLASS="program">&nbsp; </P>

    <P CLASS="program">for theta in arange(0., 2.*pi, pi/100.): </P>

<P CLASS="program">

	# see &quot;lists&quot; above</P>

<P CLASS="Normal">

You can restart a loop, or terminate the loop prematurely:</P>

    <P CLASS="program"> if a == b: continue # go back to the start of the loop</P>

    <P CLASS="program"> if a &gt; b: break # exit the loop</P>

    <P CLASS="program">&nbsp;</P>

</DIV>

<DIV>

    <H3 CLASS="Heading2"> <font color="#0000A0">Printing results</font></H3>

<P CLASS="Normal">

To print a number, a vector, a list, or anything else, use the &quot;print&quot; command:</P>

    <P CLASS="program"> print Europa.momentum</P>

<P CLASS="Normal">

To print a text message, enclose it in quotes:</P>

    <P CLASS="program"> print &quot;We have just crashed on the Moon with speed&quot;, 

      v, &quot;m/s.&quot;</P>

    

    <h3 class="Heading2"><font color="#0000A0">More Information about Python</font></h3>

    <p>See <a href="index.html">The Visual Module of VPython</a> for detailed 

      descriptions of all aspects of Visual.</p>

    <p>We have summarized a very small subset of the Python programming language. 

      Extensive <a href="../index.html">Python Documentation</a> is provided 

      here, and there is additional information at the <a href="http://www.python.org/">Python 

      website</a>, but much of this information assumes that you already have 

      lots of programming experience in other languages. We recommend the following 

      book to those who want to learn more about Python: <i>Learning Python</i>, 

      by Mark Lutz &amp; David Ascher, 1999, O'Reilly.</p>

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