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<html>
<head>
<title>Developer's Guide: Point Objects
</title>
</head>
<body bgcolor=white text=black link=blue vlink=navy alink=red>
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<TD ALIGN="left"><A HREF="devguide-4.html">Coordinate Systems
</A></TD>
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<TD ALIGN="right"><A HREF="devguide-6.html">Rect Objects
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<HR NOSHADE>
<H2><FONT face="Helvetica,Arial"><A NAME="N1"></A>Point Objects
</font></H2>
<P>Point objects represent 2D points or vectors--depending on how you
interpret them; their internal representation is identical.</P>
<P>While such points could be represented by Python tuples, this special
object type requires less memory and overloads some arithmetic
operators. A point object is represented by two C `float' numbers, one
for each cartesian coordinate.</P>
<P>Point objects are immutable.</P>
<H3><FONT face="Helvetica,Arial"><A NAME="N2"></A>Constructors</font></H3>
<P>There are two constructor functions:</P>
<P>
<DL>
<DT><B><A NAME="N3"></A><tt>Point(<i>x</i>, <i>y</i>)</tt></B><DD>
<DT><B><A NAME="N4"></A><tt>Point(<i>sequence</i>)</tt></B><DD>
<P>Return a point object with the coordinates <i>x</i> and <i>y</i>.
If called with one argument, the argument must be a sequence of
two numbers. This form is called a <A HREF="#N11">PointSpec</A></P>
<DT><B><A NAME="N5"></A><tt>Polar(<i>r</i>, <i>phi</i>)</tt></B><DD>
<DT><B><A NAME="N6"></A><tt>Polar(<i>phi</i>)</tt></B><DD>
<P>Return a point object for the polar coordinates <i>r</i> and
<i>phi</i>. If <i>r</i> is omitted, it defaults to 1.0.</P>
</DL>
</P>
<H3><FONT face="Helvetica,Arial"><A NAME="N7"></A>Attributes</font></H3>
<P>A point object has two (read only) attributes:
<DL>
<DT><B><CODE>x</CODE></B><DD>
<P>The X-coordinate of the point as a python float</P>
<DT><B><CODE>y</CODE></B><DD>
<P>The Y-coordinate of the point as a python float</P>
</DL>
</P>
<H3><FONT face="Helvetica,Arial"><A NAME="N8"></A>Methods</font></H3>
<P>A point object has these methods:</P>
<P>
<DL>
<DT><B><tt>normalized()</tt></B><DD>
<P>Return a unit vector pointing in the same direction. If the
point's length is 0, raise a ZeroDivisionError.</P>
<DT><B><tt>polar()</tt></B><DD>
<P>Return a tuple <CODE>(<i>r</i>, <i>phi</i>)</CODE> containing the polar
coordinates of the point. <i>phi</i> is in the range -pi to pi.
If <i>r</i> is 0, so is <i>phi</i>.</P>
</DL>
</P>
<H3><FONT face="Helvetica,Arial"><A NAME="N9"></A>Operators</font></H3>
<P>Point objects implement both the number and the sequence protocol for
Python objects. This allows the following operations:
<DL>
<DT><B>Number Protocol</B><DD>
<P>
<DL>
<DT><B><CODE>+<i>P</i></CODE></B><DD>
<P>The same as <i>P</i>.</P>
<DT><B><CODE>-<i>P</i></CODE></B><DD>
<P>The negated vector <i>P</i>. The same as</P>
<P><CODE>Point(-<i>P</i>.x, -<i>P</i>.y)</CODE></P>
<DT><B><CODE><i>P1</i> + <i>P2</i></CODE></B><DD>
<P>The sum of the vectors <i>P1</i> and <i>P2</i>. The same as</P>
<P><CODE>Point(<i>P1</i>.x + <i>P2</i>.x, <i>P1</i>.y + <i>P2</i>.y)</CODE></P>
<DT><B><CODE><i>P1</i> - <i>P2</i></CODE></B><DD>
<P>The difference of the vectors <i>P1</i> and <i>P2</i>. The same as</P>
<P><CODE>Point(<i>P1</i>.x - <i>P2</i>.x, <i>P1</i>.y - <i>P2</i>.y)</CODE></P>
<DT><B><CODE><i>P1</i> * <i>P2</i></CODE></B><DD>
<P>The dot product of the vectors <i>P1</i> and <i>P2</i>. The
same as</P>
<P><CODE><i>P1</i>.x * <i>P2</i>.x + <i>P1</i>.y * <i>P2</i>.y</CODE></P>
<DT><B><CODE><i>NUMBER</i> * <i>P</i></CODE></B><DD>
<DT><B><CODE><i>P</i> * <i>NUMBER</i></CODE></B><DD>
<P>The same as</P>
<P><CODE>Point(<i>NUMBER</i> * <i>P</i>.x, <i>NUMBER</i> * <i>P</i>.y)</CODE></P>
<DT><B><CODE><i>P</i> / <i>NUMBER</i></CODE></B><DD>
<P>The same as</P>
<P><CODE>Point(<i>P</i>.x / <i>NUMBER</i>, <i>P</i>.y / <i>NUMBER</i>)</CODE></P>
<DT><B>abs(<i>P</i>)</B><DD>
<P>The length of the vector <i>P</i>. The same as
<CODE>math.hypot(<i>P</i>.x, <i>P</i>.y)</CODE>.</P>
</DL>
</P>
<DT><B>Sequence Protocol</B><DD>
<P>
<DL>
<DT><B><CODE>len(<i>P</i>)</CODE></B><DD>
<P>Always returns 2.</P>
<DT><B><CODE><i>P</i>[<i>i</i>]</CODE></B><DD>
<P>For <CODE><i>i</i></CODE> either 0 or 1, this is the same as
<CODE><i>P</i>.x</CODE> or <CODE><i>P</i>.y</CODE> respectively. For other values
of <i>i</i> raise an IndexError exception.</P>
<DT><B><CODE>tuple(<i>P</i>)</CODE></B><DD>
<P>Return the coordinates of <i>P</i> as a tuple <CODE>(<i>P</i>.x,
<i>P</i>.y)</CODE>.</P>
<DT><B><CODE>x, y = <i>P</i></CODE></B><DD>
<P>Unpack the point <CODE><i>P</i></CODE>. Equivalent to <CODE>x, y =
tuple(<i>P</i>)</CODE></P>
</DL>
</P>
</DL>
</P>
<P><i>P</i>, <i>P1</i> and <i>P2</i> are point objects, <i>NUMBER</i> is any
number that can be converted to a float.</P>
<P><CODE>abs</CODE>, <CODE>tuple</CODE>, <CODE>len</CODE> and <CODE>math.hypot</CODE> are the standard
Python functions of that name.</P>
<H3><FONT face="Helvetica,Arial"><A NAME="N10"></A>Constants</font></H3>
<P>
<DL>
<DT><B><CODE>NullPoint</CODE></B><DD>
<P>This is <CODE>Point(0, 0)</CODE></P>
<DT><B><CODE>PointType</CODE></B><DD>
<P>The point type object.</P>
</DL>
</P>
<H3><FONT face="Helvetica,Arial"><A NAME="N11"></A>PointSpec
</font></H3>
<P>While point objects are the standard representation for a point, it is
sometimes inconvenient (particularly if you are computing the individual
coordinates separately) to create a point object just because a function
requires that argument type. Therefore, some functions also accept a
<EM>PointSpec</EM> instead.</P>
<P>An argument that is supposed to be a PointSpec can be either a point
object or any sequence of two numbers. Here, number means any object
that can be converted to a `double' in C. You could use e. g. a tuple of
floats or ints instead of a point object.</P>
<HR NOSHADE>
<TABLE WIDTH="100%">
<TR>
<TD ALIGN="left"><A HREF="devguide-4.html">Coordinate Systems
</A></TD>
<TD ALIGN="center"><A HREF="devguide-4.html">Coordinate Systems
</A></TD>
<TD ALIGN="right"><A HREF="devguide-6.html">Rect Objects
</A></TD>
</TR>
<TR>
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